NEtwork Analysis Lab Manual

Department of Electrical Engineering

Network Analysis Lab Manual

TABLE OF LAB EXPERIMENTS Sr. Sr . No.

Objectives

P age N o.

To verify maximum power transfer theorem. 1.

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To observe effect of source and load resistance on efficiency. To verify Thevenin theorem. 2.

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To draw Thevenin equivalent of a passive resistive network.

3.

To analyze analyze response response of 1st order RC differentiator differentiator network different inputs and at different frequencies.

for

4.

To analyze response of 1st order RC integrator network for different inputs and at different frequencies.

6.

To study the transient response of a series RC circuit. To differentiate between steady state and transient response. To understand time constant concept using step input. To find actual value of a capacitor. To study the characteristics and frequency response of passive low pass filter.

7.

To study the characteristics and frequency response of passive high pass filter.

5.

14

19

23

28

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To observe resonance phenomenon in electrical networks and study its effects. 8.

To determine the resonant frequency and bandwidth of the given network using a sinusoidal input.

9.

To design a band pass filter with pass band (130 Hz -2 kHz) and observe its amplitude response. To observe frequency response of a band stop filter.

10.

To observe sinusoidal steady state response of an electrical network.


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41 44 47

3

11.

To determine complex impedance, and power factor of a network. To grasp the concept of active, reactive and apparent power . To differentiate between reciprocal and non-reciprocal networks.

12.

To verify reciprocity theorem.

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13.

To learn DC analysis, AC analysis and transient analysis anal ysis of electrical networks using PSpice.

55

14.

To learn modeling of electrical networks in frequency domain using Matlab symbolic toolbox.

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To determine two port network z parameters. p arameters. 15.

To determine two port network y parameters.

84

Additional Tasks as per Lab Instructor’s Desire


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PREFACE With the name Almighty Allah who made it possible for me to revise this manual. The laboratory of every subject taught in the degree of Bachelors in Electrical Engineering is of significance importance in every university. Fully equipped laboratories meeting the industrial demands under the supervision of qualified, talented and practically motivated lab assistants and lab engineers are also a basic criterion of the Pakistan Engineering Council Co uncil for accrediting an engineering program. Laboratory of network analysis course is very important as many physical systems can be modeled in the form of electrical networks. Once model is correctly designed, one can implement the physical system with actual components. The experiments covered in this lab will help students in testing the actual response of network models. Some computer aided techniques of network analysis are also covered in the manual. The revision of lab manuals is a constant process as technologies keep on changing. All suggestions and criticisms for the improvement of lab experiments and their conduction will be warmly welcomed.

With Regards

Engr. Nayab Asif May 2012


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General Lab Instructions      

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Each student group consists of 2-4 students. Each group member is responsible in submitting lab report upon completion of each experiment. Students are to wear proper attire i.e. shoe or sandal instead of slipper. Excessive jewelries are not allowed as they might cause electrical shocks. A permanent record in ink of observations as well as results should be maintained by each student enclosed with the report. The recorded data and observations from the lab manual need to be approved and signed by the lab instructor upon completion of each experiment. Before beginning connecting up, it is essential to check that all sources of supply at the bench are switched off. Start connecting up the experiment circuit by wiring up the main circuit path, then adds the parallel branches as indicated in the circuit diagram.

After the circuit has been connected correctly, remove all unused leads from the experiment area, set the voltage supplies at the minimum value, and check the meters are set for the intended mode of operation. The students may ask the lab instructor to check the correctness of their circuit before switching on.

When the experiment has been satisfactory completed and the results approved by the instructor, the students may disconnect the circuit and return the components and instruments to the locker tidily. Chairs are to be slid in properly.


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Experiment No. 1 MAXIMUM POWER TRANSFER THEOREM OBJECTIVE To verify maximum power transfer theorem. To observe effect of source and load resistance on efficiency.

THEORY The maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must be equal to the resistance of the source as viewed from the output terminals. The maximum amount of power will be dissipated in the load resistance if it is equal in value to the Thevenin or Norton source resistance of the network supplying the power. The theorem results in maximum power transfer, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source, then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance goes up. If the load resistance is smaller than the source resistance, then most of the power ends up being dissipated in the source, and although the total power dissipated is higher, due to a lower total resistance, it turns out that the amount dissipated in the load is reduced. The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given, not the opposite. It does not say how to choose the source resistance, once the load resistance is given. Given a certain load resistance, the source resistance that maximizes power transfer is always zero, regardless of the value of the load resistance. The theorem can be extended to AC circuits that include reactance, and states that maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance. The theorem was originally misunderstood (notably by Joule) to imply that a system consisting of an electric motor driven by a battery could not be more than 50% efficient since, when the impedances were matched, the power lost as heat in the battery would always be equal to the power delivered to the motor. To achieve maximum efficiency, the resistance of the source (whether a battery or a dynamo) could be made close to zero. Using this new understanding, they obtained an efficiency of about 90%, and proved that the electric motor was a practical alternative to the heat engine.


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Figure 1: Maximum Power Transfer Theorem

Figure 2: Graph Illustrating Maximum Power Transfer Theorem

As in Figure 2, condition of maximum power transfer does not result in maximum efficiency. If we define the efficiency η as the ratio of power dissipated by the load to power developed by the source, then it is straightforward to calculate from the above circuit diagram that

η= R load / (R source+ R load) = 1 / {(R source/ R load) + 1} Consider three particular cases: If R load=R source , then η=0.5 If R load=∞ or R source=0, then η=1 If R load=0, then η=0 The efficiency is only 50% when maximum power transfer is achieved, but approaches 100% as the load resistance approaches infinity, though the total power level tends towards zero. Efficiency also approaches 100% if the source resistance can be made close to zero. When the load resistance is zero, all the power is consumed inside the source (the power dissipated in a short circuit is zero) so the efficiency is zero.


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EQUIPMENT DC power supply

Breadboard

Digital multimeter

Resistors (1kΩ, 1.5 kΩ, 2 kΩ, 2.7 kΩ,3 kΩ, 3.3 kΩ, 4.3 kΩ, 5.6 kΩ, 7.5 kΩ, 10 kΩ)

Jumpers wires

CIRCUIT DIAGRAM

PROCEDURE 1. Connect the components on bread board according the circuit diagram.

2. Measure VL, load voltage and IL, load current, across each resistor. 3. Put these observed value in Table 1. 2

4. Calculate PL, load power using PL=I R L or PL=VL*IL 5. Draw a graph between R L and PL. 6. Observe the pair that has maximum power output.

Results Measured data R L (k ) VL (V) IL (mA) PL (mW)

Graph between R L and PL Graph between R L and η


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DISCUSSION 1. How will you relate maximum power transfer theorem with impedance matching principle?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 2. If circuit is reactive not resistive, how will you implement maximum power transfer?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


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Experiment No. 2 THEVENIN THEOREM OBJECTIVE To verify Thevenin theorem. To draw Thevenin equivalent of a passive resistive network.

THEORY Any two terminal, bilateral, linear networks can be replaced by an equivalent voltage source in series with an equivalent resistance connected across the load. The load current is given by IL = VTH / (R TH+R L)

EQUIPMENT Power supply

Variable resistor

Digital multimeter

Jumper wires

Resistors: 10KΩ (3), 4.7 KΩ, 1 KΩ

Bread board

CIRCUIT DIAGRAM

Figure 1: Actual Network


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Figure 2: Measuring VTH

Figure 3: Finding R TH

Figure 4: Thevenin Equivalent Circuit

PROCEDURE 1. Connect the components as shown in Figure 1. 2. Measure the voltage (VL1) and current (IL1) in 1 kΩ resistance and note these values. 3.

Remove 1 kΩ resistor as shown in Figure 2 and find VTH across the open circuit terminals from where 1 kΩ was removed.

4. Connect the circuit according to Figure 3 and measure the current I to find R TH. 5. Now connect the circuit as shown in Figure 4 by changing resistance of variable resistor equal to R TH and voltage of power supply adjusted to VTH. 6. With this Thevenin equivalent circuit, measure the voltage (VL2) and current (IL2) in 1 kΩ resistance and note these values. 7. Compare VL2 and IL2 with VL1 and current IL1. If these values are same, Thevenin theorem is verified.

RESULTS VL1= IL1= VTH= R TH= VL2= IL2= Network Analysis Lab Manual

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DISCUSSION 1. What can be application of Thevenin theorem for maximum power transfer to load?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


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Experiment No. 3 1ST ORDER RC DIFFERENTIATOR CIRCUIT OBJECTIVE To analyze response of 1st order RC differentiator network for different inputs and at different frequencies.

THEORY The voltage (Vc) and current ( I c) relationship for capacitor is by I c(t)=C.dVC/dt

This relationship is helpful in implementing a passive differentiator circuit. For an RC series network to work as an integrator R << X C i.e. voltage drop across resistor is very small and VIN≈ VC. The tentative output of RC network at ω << 1/RC is shown in Figure. Here ω is the frequency of input waveform. The said condition on frequency assures that capacitor has time to charge up until its voltage is almost equal to input voltage.

Figure 1: RC Diffrentiator

KVL equation for the network will be, VIN=VR + VC VR = R I = RC . dVC/dt Since VIN≈ VC ,Therefore VR≈ RC . dVIN/dt Thus the output voltage is somehow derivative of input voltage.

EQUIPMENT Function generator

Bread board

Oscilloscope

Jumper wires

Probes

Capacitor: 0.33μF


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Resistor: 1kΩ CIRCUIT DIAGRAM

PROCEDURE 1. Connect the components as shown in Figure. 2. Apply a square waveform of 6 V peak to peak from function. 3. Observe the input waveform and response simultaneously on oscilloscope when T<>RC where T is the period of input waveform. 8. Save this waveform in USB from oscilloscope and insert in results after taking the printout. 9. Repeat the same steps for a triangular waveform. 10. Repeat same steps for sinusoidal waveform.

RESULTS Graphs of Input and Output For Square Input (i) T<>RC Graphs of Input and Output For Triangular Input (i) T<
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(iii)T>>RC Graphs of Input and Output For Sinusoidal Input (i) T<>RC

DISCUSSION 1. If the following input is given to differentiator circuit, what will be the output waveform? Draw the ideal and practical waveforms.

2. An electronics technician needs a simple circuit that outputs brief pulses of voltage every time a switch is actuated, so that a computer receives a single pulse signal every time the

switch is actuated, rather than a continuous “on” signal for as long as the switch is actuated. He tells you it is perfectly okay if the circuit generates negative voltage pulses when the switch is de-actuated: all he cares about is a single positive voltage pulse to the computer each time the switch actuates. Also, the pulse needs to be very short: no longer than 2 milliseconds in duration. Given this information, draw a schematic diagram for a practical passive differentiator circuit within the dotted lines, complete with component values.

3. Plot the output waveform of a passive differentiator circuit, assuming the input is a symmetrical square wave and the circuit‟s RC time constant is about one-fifth of the

square wave‟s pulse width. Network Analysis Lab Manual

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4. Potentiometers are very useful devices in the field of robotics, because they allow us to represent the position of a machine part in terms of a voltage. In this particular case, a potentiometer mechanically linked to the joint of a robotic arm represents that arm‟s angular position by outputting a corresponding voltage signal. As the robotic arm rotates up and down, the potentiometer wire moves along the resistive strip inside, producing a voltage directly proportional to the arm‟s position. A voltmeter connected between the potentiometer wiper and ground will then indicate arm position. A computer with an analog input port connected to the same points will be able to measure, record, and (if also

connected to the arm‟s motor drive circuits) control the arm‟s position.

If we connect the potentiometer‟s output to a differentiator circuit, we will obtain another signal representing something else about the robotic arm‟s action. What physical variable does the differentiator output signal represent?


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5. Calculate the output voltage of this passive differentiator circuit 150 microseconds after

the rising edge of each ”clock” pulse (where the square wave transitions from 0 volts to +5 volts).

6. An LR differentiator circuit is used to convert a triangle wave into a square wave. One day after years of proper operation, the circuit fails. Instead of outputting a square wave, it outputs a triangle wave, just the same as the waveform measured at the circuit‟s input. Determine what the most likely component failure is in the circuit.


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Experiment No. 4 1ST ORDER RC INTEGRATOR CIRCUIT OBJECTIVE To analyze response of 1st order RC integrator network for different inputs and at different frequencies.

THEORY The voltage (Vc) and current (Ic) relationship for capacitor is by Vc(t)=1/C. ∫ Ic dt This relationship is helpful in implementing a passive integrator circuit. For an RC series network to work as an integrator R >> XC i.e. voltage drop across capacitor is very small and VIN≈ VR . The tentative output of RC network at ω >> 1/RC is shown in Figure. Here ω is the frequency of input waveform. The said condition on the frequency of input waveform assures that capacitor does not have sufficient time to charge up, therefore its voltage is very small and resistor voltage is almost equal to input voltage.

Figure 1: RC Integrator

KVL equation for the network will be, VIN=VR + VC Since VIN≈ VR , therefore, I=VR /R = VIN/R As Vc(t)=1/C. ∫ I dt , Vc(t)=1/RC. ∫ VIN dt Thus the output voltage across capacitor is somehow integration of the input voltage.


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Jumper wires

Oscilloscope

Capacitor : 0.33μF

Probes

Resistor: 1kΩ

Bread board

CIRCUIT DIAGRAM

PROCEDURE 1. Connect the components as shown in Figure. 2. Apply a square waveform of 6 V peak to peak from function. 3. Observe the input waveform and response simultaneously on oscilloscope when T>>RC where T is the period of input waveform. 4. Save this waveform in USB from oscilloscope and insert in results after taking the print out. 5. Observe the input waveform and response simultaneously on oscilloscope when T=RC where T is the period of input waveform. 6. Save this waveform in USB from oscilloscope and insert in results after taking the print out. 7. Observe the input waveform and response simultaneously on oscilloscope when T<
RESULTS Graphs of Input and Output for Square Input (i) T>>RC (ii) T=RC Network Analysis Lab Manual

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(iii)T<>RC (ii) T=RC (iii)T<>RC (ii) T=RC (iii)T<
DISCUSSION 1.

Design a passive integrator circuit using a resistor and inductor rather than a resistor and capacitor . In addition to completing the inductor circuit schematic, qualitatively state the preferred values of L and R to achieve an output waveform most resembling a true triangle wave. In other words, are we looking for a large or small inductor; a large or small resistor?

2. Determine what the response will be to a constant DC voltage applied at the input of these (ideal) circuits.


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3. A passive integrator circuit is energized by a square wave signal with peak-to-peak amplitude of 12 volts and a frequency of 65.79 Hz. Determine the peak-to-peak voltage of the output waveform.

4. Draw the intermediate response shown by the oscilloscope for following figure.


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Experiment No. 5 TRANSIENT RESPONSE OF RC SERIES NETWORK OBJECTIVE To study the transient response of a series RC circuit. To differentiate between steady state and transient response. To understand time constant concept using step input. To find actual value of a capacitor.

THEORY For the RC network of Figure 1, voltage VC(t) across the capacitor is given by

where, V is the applied source voltage to the circuit for t ≥ 0. RC = τ is the time constant. The response curve is increasing and is shown in Figure 2.

Figure 1: RC Series Network

Figure 2: Capacitor Charging

The discharge voltage for the capacitor is given by


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where Vo is the initial voltage stored in capacitor at t = 0, and RC = τ is time constant. The response curve is a decaying exponentials as shown in Figure 3.

Figure 3: Discharging of Capacitor

EQUIPMENT Power supply

Jumper wires

Oscilloscope

Resistor: 220 kΩ

Probes

Capacitor: 470µF

Bread board

Digital multimeter

Stop watch

CIRCUIT DIAGRAM

i(t)

Figure 4: Capacitor Charging

i(t)

Figure 5: Capacitor Discharging


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PROCEDURE 1. Connect the components on bread board according the circuit diagram shown in Figure 4. 2. Find actual value of 220 kΩ resistor by multimeter. 3. Apply step input voltage of 5 V from power supply. As soon as power supply is switched on, start the stop watch. 4. Note down the values of capacitor voltage (VC) and resistor voltage (VR ) at different time instants. 5. Current i(t) can be either found by VR /R measuring its voltage by oscilloscope.

or by inserting an extra 1Ω resistance and

6. Specially note the time reading when capacitor voltage becomes 63% of input voltage i.e. 3.15 V. 7. Take the readings at regular time intervals until capacitor is fully charged up to the supply voltage. 8. Note down the time when capacitor voltage reaches to 98% of the supply voltage i.e. when VC=4.9 V. This usually takes place after 5RC. 9. Now draw the graphs of VC, VR and i (all versus time). 10. Now connect the components on bread board according the circuit diagram shown in Figure 5 and start the stop watch. 11. Note down the values of capacitor voltage (VC) and resistor voltage (VR ) at different time instants. 12. Observe the value of current i(t). Current i(t) can be either found by VR /R or by inserting

an extra 1Ω resistance and measuring its voltage by oscilloscope. Actual direction of current flow will be opposite to that shown In Figure 5. 13. Take the readings at regular time intervals until capacitor is fully discharged up to the zero volts. This usually takes place after 5RC. 14. Now draw the graphs of VC, VR and i (all versus time). 15. Find the actual value of capacitor in μF by using your observations.

RESULTS For Capacitor Charging Sr. No. 1

t

VC (t)

VR (t)

i (t)

2 3 4 5 6


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7 8 9 10 11 12 13 14 15

Graphs for Charging

Graph between VC and t Graph between VR and t Graph between i and t Value of Time Constant= Actual value of capacitor= For Capacitor Discharging Sr. No. 1

t

VC (t)

VR (t)

i (t)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 Network Analysis Lab Manual

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Graphs for Discharging

Graph between VC and t Graph between VR and t Graph between i and t

DISCUSSION 1. Differentiate between natural and forced response.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 2. Differentiate between transient and steady state response.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 3. Define time constant. What is its value for RL network?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


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Experiment No. 6 LOW PASS FILTER OBJECTIVE To study the characteristics and frequency response of passive low pass filter.

THEORY The impedance of an inductor is proportional to frequency and the impedance of a capacitor is inversely proportional to frequency. These characteristics can be used to select or reject certain frequencies of an input signal. This selection and rejection of frequencies is called filtering, and a circuit which does this is called a filter. If a filter passes low frequencies and rejects high ones, it is called a low-pass filter. An RC low pass filter is shown in Figure 1.

Figure 1: Low Pass Filter

Filters, like most things, aren‟t perfect. They don‟t absolutely pass some frequencies and absolutely reject others. A frequency is considered passed if its magnitude (voltage amplitude) is within 70% (or 1/√2) of the maximum amplitude passed and reject ed otherwise. The 70% frequency is called corner frequency, roll-off frequency, break frequency, cutoff frequency or half-power frequency. The corner frequency for the RC filter is given as: f C = 1 / 2πRC

At cut off frequency, R=XC i.e. voltage VR =VC and phase angle between input and output voltage will be 450.


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Figure 2: Amplitude and Phase Response of Low Pass RC Filter


Jumper wires

Oscilloscope

Resistor: 1.2kΩ

Probes

Capacitor: 1µF

Bread board

CIRCUIT DIAGRAM 1.2 kohm AC Voltage Source 1 micro farad

PROCEDURE 1. Connect the components on bread board according the circuit diagram. 2. Apply sinusoidal input voltage of 5 V peak to peak with 20 Hz frequency from function generator and note the peak to peak voltage across capacitor from oscilloscope. 3. Also measure the phase difference (“θ”) between input and output voltage by oscilloscope. 4. Increase the frequency at regular steps and fill the table shown below. 5. Draw the graph between output voltage and frequency. 6. Mark the cut off frequency on the graph. 7. Draw the graph between θ and frequency. 8. Mark the value of θ at cut off frequency.


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RESULTS Sr. No.

Peak to peak value of input voltage

Frequency of input voltage (Hz)

Peak to peak value of output voltage from oscilloscope

Phase angle between input and output voltage

(“θ” degrees)

(V0=VC)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p

10 20 30 40 50 60 70 80 90 10 110 120 130 140

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5 V p-p

150

Graph between Output Voltage and Frequency Graph between θ and Frequency

DISCUSSION 1. Differentiate between passive and active filters?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 2. What is the ratio of output and input voltage levels in db at cutoff frequency?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… Network Analysis Lab Manual

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3. What do you mean the term frequency octave and frequency decade?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… …………………………………………………………………………………………… 4. Write some real applications in which low pass filter is used?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 5. Your viewpoint regarding the results.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


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Experiment No.7 HIGH PASS FILTER OBJECTIVE To study the characteristics and frequency response of passive high pass filter.

THEORY If a filter allows signals of higher frequencies to pass from input to the output while blocking the lower frequencies, this filter is called a high pass filter. The minimum frequency it allows to pass is called cutoff frequency f C. A high pass filter may be RL or RC as shown in Figures below. The cutoff frequency for the RC filter is given as: V0=Vi×[R/(R-jXc)] f c = 1 / 2πRC

At fc, R=Xc and the phase angle between Vo and Vi is +45 as shown in Figure 1(c).It can be seen that high pass filter can be obtained merely by interchanging the positions of R and C in low pass RC filter. In high pass filter, all the frequencies above f c are passed and below are attenuated.

Figure 1: High Pass RC Filter

The cutoff frequency for the RL filter is given as: V0=Vi×[jXL/(R+jXL)] f c = R / 2πL


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Figure 2: High Pass RL Filter


Jumper wires

Oscilloscope

Resistor: 1.2 kΩ

Probes

Capacitor: 1µF

Bread board

CIRCUIT DIAGRAM

1.2 kohm AC Voltage Source 1 micro farad

PROCEDURE 1. Connect the components on bread board according the circuit diagram. 2. Apply sinusoidal input voltage of 5 V peak to peak with 20 Hz frequency from function generator and note the peak to peak voltage across resistor from oscilloscope. 3.

Also measure the phase difference (“θ”) between input and resistor output voltage by

oscilloscope. 4. Increase the frequency at regular steps and fill the table shown below. 5. Draw the graph between output voltage and frequency. 6. Mark the cut off frequency on the graph. 7. Draw the graph between θ and frequency. 8. Mark the value of θ at cut off frequency.


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RESULTS Sr. No.



Peak to peak value of resistor output voltage from oscilloscope

Phase angle between input and output voltage

(“θ” degrees)

(V0=VR )

5 6 7 8 9 10 11 12 13 14

5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p

50 60 70 80 90 10 110 120 130 140

15

5 V p-p

150

1 2 3 4

10 20 30 40

Graph between Output Voltage (Vo) across Resistor and Frequency Graph between θ and Frequency

DISCUSSION 1. Your comments regarding the results.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


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Experiment No. 8 RESONANCE PHENOMENON IN ELECTRICAL NETWORKS OBJECTIVE To observe resonance phenomenon in electrical networks and study its effects. To determine the resonant frequency and bandwidth of the given network using a sinusoidal input.

THEORY A resonant circuit, also called a tuned circuit consists of an inductor and a capacitor together with a voltage or current source. It is one of the most important circuits used in electronics. For example, a resonant circuit, in one of its many forms, allows us to select a desired radio or television signal from the vast number of signals that are around us at any time. A network is in resonance when the voltage and current at the network input terminals are in phase and the input impedance of the network is purely resistive.

Figure 1: Parallel Resonance Circuit

Consider the Parallel RLC circuit of Figure 1. The steady-state admittance offered by the circuit is:

Y = 1/R + j( ωC – 1/ωL) Resonance occurs when the voltage and current at the input terminals are in phase. This corresponds to a purely real admittance, so that the necessary condition is given by

ωC – 1/ωL = 0

The resonant condition may be achieved by adjusting L, C, or ω. Keeping L and C constant, the resonant frequency ωo is given by:


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Or

Frequency response is a plot of the magnitude of output Voltage of a resonance circuit as function of frequency. The response of course starts at zero, reaches a maximum value in the vicinity of the natural resonant frequency, and then drops again to zero as ω becomes infinite. The frequency response is shown in Figure 2.

Figure 2: Frequency Response of Parallel Resonant Circuit

The two additional frequencies ω1 and ω2 are also indicated which are called half-power frequencies. These frequencies locate those points on the curve at which the voltage response is 1/√2 or 0.707 times the maximum value. They are used to measure the band -width of the response curve. This is called the half-power bandwidth of the resonant circuit and is defined as:

β = ω2 - ω1

Figure 3: Series Resonance Circuit

When network of Figure 3 is in tuned condition, inductive reactance will be cancelled by capacitive reactance, therefore, impedance of the circuit will be minimum, current will be maximum and this current will be in phase with voltage i.e. power factor will be unity as shown in Figure 4.


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Figure 4: Effect of Frequency on Different Parameters


Resistors: 120 Ω, 1 Ω

Oscilloscope

Inductor: 10 mH

Bread board

Capacitor: 100 µF

Jumper wires

CIRCUIT DIAGRAM

120 o m

120 Ω 1Ω

AC Voltage Source

Series10mHRLC Branch1

100 µF

PROCEDURE 1. Connect the components on bread board according the circuit diagram. 2. Find the theoretical value of resonant frequency. 3. Apply sinusoidal voltage of 10 V peak to peak from function generator with frequency less than the resonant frequency. 4. Observe the waveforms of input voltage and current on the oscilloscope simultaneously. 5. Note down value of rms current at oscilloscope. 6. Increase the frequency gradually until the current becomes in phase with the input voltage. This frequency is the resonant frequency. 7. Increase the frequency further and see the phase difference between current and voltage waveforms. Network Analysis Lab Manual

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8. Note down values rms currents at different frequencies and plot the graph between current (I) and frequency (f).

RESULTS

Input Frequency

Current

Current Status

(f)

(I)

(Leading/ In phase/Lagging) phase/Lagging)

Sr. No.


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Voltage and current waveform on oscilloscope when f< f 0 Voltage and current waveform on oscilloscope when f=f 0 Voltage and current waveform on oscilloscope when f> f 0 Graph between current (I) and frequency (f) from the observed values

DISCUSSION 1.

What is the purpose if 1Ω resistor? ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………

2. What is the quality factor of network shown in circuit diagram?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 3. What do you mean by the term “selectivity”? ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 4. Actual results in frequency dependent networks may vary from the theoretical ones? Comment.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


40

5. What are the different applications of resonance?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


41

Experiment No. 9 BAND PASS FILTER OBJECTIVE To design a band pass filter with pass band (130 Hz -2 kHz) and observe its amplitude response.

THEORY It is a filter that allows a certain band of frequencies to pass through and attenuates all other frequencies below and above the band. This pass band is known as the bandwidth of the filter. A passive band pass filter can be obtained by cascading a high pass RC filter to a low pass RC filter as shown in Figure 1.

Figure 1: Band Pass Filter

The pass band of the filter is given by the band of frequencies lying between f c1 and f c2. The value of f c1 is determined by the high pass filter and f c2 by low pass filter. Their values are given by f c1 = 1 / 2πR 1C1 and f c 2= 1 / 2πR 2C2


Jumper wires

Oscilloscope

Two resistors as per design

Probes

Two capacitors as per design

Bread board


42

CIRCUIT DIAGRAM Draw the circuit diagram as per designed values of capacitors and resistors. Also write your design calculations.

PROCEDURE 1. Connect the components on bread board according the circuit diagram. 2. Apply sinusoidal input voltage of 5 V peak to peak with 10 Hz frequency from function generator and note the peak to peak output voltage from oscilloscope. 3. Increase the frequency of input waveform gradually from the function generator and fill the table shown below. 4. Draw the graph between output voltage and frequency. 5. Mark the cut off frequencies on the graph. 6. Determine the bandwidth of the filter.

RESULTS Sr. No.

1 2 3 4 5 6 7 8 9 10 11



5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p

10


Peak to peak value of output voltage from oscilloscope

20.log(V 0/Vi)

db

50 100 150 200 300 500 600 800 1000 1200 43

12 13 14 15 16 17 18 19 20 21 22

5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p 5 V p-p

1400 1600 1800 2000 2200 2400 2600 2800 3000 3500 4000

Practical Bandwidth =…………………… Graph between 20log (V 0/Vi) and Frequency


……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


44

Experiment No. 10 BAND STOP FILTER OBJECTIVE To observe frequency response of a band stop filter.

THEORY It is a filter that attenuates a certain band of frequencies and allows all other frequencies to pass. This stop band is known as the bandwidth of the filter. The series resonance circuit can also be used as a band stop filter. The center frequency of the circuit is given by


Jumper wires

Oscilloscope

Resistor: 680Ω

Probes

Capacitor:10nF

Bread board

Inductor: 100mH

CIRCUIT DIAGRAM

PROCEDURE 1. Connect the components on bread board according the circuit diagram.


45

2. Apply sinusoidal input voltage of 1 V rms with center frequency from function generator. At center frequency output voltage would be minimum. 3. Decrease the frequency of input waveform less than center frequency from the function generator and note the frequency when output voltage becomes 70.7% of the input voltage. This frequency is called f1. 4. Increase the frequency of input waveform less than center frequency from the function generator and note the frequency when output voltage becomes 70.7% of the input voltage. This frequency is called f2. 5. Draw the graph between output voltage (db) and frequency. 6. Determine the bandwidth (f2-f1) of the filter.

RESULTS Sr. No.

RMS value of input voltage

1 2 3 4 5

1V 1V 1V 1V 1V 1V 1V 1V 1V 1V 1V 1V

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

1V 1V 1V 1V 1V 1V 1V 1V 1V 1V 1V



RMS value of output voltage from oscilloscope

20.log [Vout] db

f c=………..

46

24

1V

25

1V

f 1=…………………

f 2=…………………..

Practical Bandwidth (f 2-f 1) =…………………… Graph between Output Voltage (Vo in dB) and Frequency (Hz)

(Use logarithmic graph paper)


……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………


47

Experiment No. 11 SINUSOIDAL STEADY STATE RESPONSE OBJECTIVE To observe sinusoidal steady state response of an electrical network. To determine complex impedance, and power factor of a network. To grasp the concept of active, reactive and apparent power.

THEORY If a sinusoidal source is connected to a network of linear passive elements, then every voltage and current in that network will be sinusoidal in the steady state, differing from the source waveform in amplitude and phase angle. The input and steady state output of a physical circuit is shown in Figure 1.

Figure 1: Sinusoidal Steady State Response

Impedance and admittance values of common circuit elements are shown in the following Table 1.

Table 1: Parameters for Network Elements

A passive RC network is shown in Figure 2. The input impedance of a circuit is defined as the ratio of input voltage to input current. Mathematically,


48

If φ is the phase difference between VIN and IIN then is called the power factor and different powers consumed in the network are defined as, Active Power: P = VIN (rms)IIN(rms) Cos φ Reactive Power: Q = VIN(rms)IIN(rms) Sin φ

(Watts) (Vars) 2

2

S = VIN(rms) IIN(rms) =√(P +Q )

Apparent Power:

(VA)

S = P+jQ= (1/2)(V)(I *) = VrmsI*rms = I2rms Z = V2rms/Z

In complex form,

Figure 2: RC Network

If waveforms of the VIN and IIN are simultaneously observed on the oscilloscope as shown in Figure 3, then phase difference φ between VIN and IIN can be found as

Figure 3: Measuring Phase Difference between Two Waveforms


Jumper wires

Oscilloscope

Resistor: 1kΩ

Probes

Capacitor: 1μF

Bread board


Resistor:1Ω

49

CIRCUIT DIAGRAM

PROCEDURE 1. Connect the components on bread board according the circuit diagram. 2. Apply sinusoidal input voltage of 3 V rms with 50 Hz frequency from function generator. Take VIN as refrence i.e. VIN= (√2)(3) ˂ 00. 3. Measure the peak values of input voltage and current from the oscilloscope. Also measure the phase difference between the said waveforms. 4. Note the readings in the table. 5. Save the waveforms displayed on the oscilloscopes in your flash RAM (USB) and insert in your manual after taking the printout. 6.

Now see waveforms of voltage across 1 kΩ resistor (VR ) and its current (IR) simultaneously on oscilloscope and save in your USB to insert in manual.

7.

Now see waveforms of voltage across 1 μF capacitor (VC) and its current (IC)

simultaneously on oscilloscope and save in your USB to insert in manual. 8. Note the readings in the table. 9. Repeat the same procedure at 200 Hz, 500 Hz and 1 kHz.

RESULTS 50 Hz Input Voltage Phase Difference(φ) between VIN and IIN

200 Hz 0

4.24 ˂ 0

500 Hz 0

4.24 ˂ 0

1 kHz 0

4.24 ˂ 0

0

4.24 ˂ 0

(360.∆T/T)

Input current in polar form Input Impedance in polar form Network Analysis Lab Manual

50

Power factor (Cos φ) Leading /Lagging Active power (P) Reactive Power (Q) Apparent Power (S) At 50 Hz frequency Graph between input voltage and current saved from oscilloscope Vector representation of input voltage and input current Graph between 1 kΩ resistor (VR ) and its current (IR ) saved from oscilloscope Vector Representation of V R and IR (Take VR at horizontal axis) Graph between 1 μF capacitor (VC) and its current (IC)) saved from oscilloscope Vector Representation of VC and IC (Take VC at horizontal axis) At 200 Hz frequency Graph between input voltage and current saved from oscilloscope Vector representation of input voltage and input current Graph between 1 kΩ resistor (VR ) and its current (IR ) saved from oscilloscope Vector Representation of V R and IR (Take VR at horizontal axis) Graph between 1 μF capacitor (VC) and its current (IC)) saved from oscilloscope Vector Representation of VC and IC (Take VC at horizontal axis) At 500 Hz frequency Graph between input voltage and current saved from oscilloscope Vector representation of input voltage and input current Graph between 1 kΩ resistor (VR ) and its current (IR ) saved from oscilloscope Vector Representation of V R and IR (Take VR at horizontal axis) Gra ph between 1 μF capacitor (VC) and its current (IC)) saved from oscilloscope Vector Representation of VC and IC (Take VC at horizontal axis) At 1 kHz frequency Graph between input voltage and current saved from oscilloscope Vector representation of input voltage and input current Graph between 1 kΩ resistor (VR ) and its current (IR ) saved from oscilloscope Vector Representation of V R and IR (Take VR at horizontal axis) Graph between 1 μF capacitor (VC) and its current (IC)) saved from oscilloscope Vector Representation of VC and IC (Take VC at horizontal axis)


51

DISCUSSION 1. Define susceptance?

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 2. Suppose an electrical network draws 1A rms current. Write this current in polar form if p.f. is (i) 0.8, lagging (ii) 0.8, leading (iii) unity

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 3. Suppose an inductive network draws 1 kW and 2 kVA. What will be power factor and reactive power drawn by the network? Also write apparent power in P ± jQ form.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………


52

Experiment No. 12 RECIPROCITY THEOREM OBJECTIVE To differentiate between reciprocal and non-reciprocal networks. To verify reciprocity theorem.

THEORY Any network composed of linear, bilateral elements (such as R, L and C) is reciprocal. The reciprocity theorem states that if an emf E in one branch of a reciprocal network produces a current I in another, then if the emf E is moved from the first to the second branch, it will cause the same current in the first branch, where the emf has been replaced by a short circuit. The ratio E/I is known as transfer resistance or impedance (Z) in AC networks. The reciprocity theorem is applicable only to single-source networks containing no time varying elements. When applying reciprocity theorem for a voltage source, following steps must be taken:-





Voltage source is replaced by a short circuit in original location.

Polarity of source in new location is such that the current direction in that branch remains unchanged.

Figure 1: Reciprocity Theorem


Bread board

Oscilloscope

Jumper wires

Probes

Resistors: 1kΩ, 2 kΩ, 4.7kΩ


53

CIRCUIT DIAGRAM

Figure 2: T-Network

Figure 3: T- Network

PROCEDURE 1. 2. 3. 4. 5. 6.

Connect the components on bread board according the circuit diagram shown in Figure 2. Apply the 5V dc supply and measure the current I1. Connect the components on bread board according the circuit diagram shown in Figure 3. Apply the 5V dc supply and measure the current I2. Compare the readings of I1 and I2 . If I1=I2, reciprocity theorem is satisfied.

RESULTS Measured values for Network of Figure 2 E

Measured values for Network of Figure 3 E

I1

I2

E/I1

E/I2

DISCUSSION 1. Differentiate between unilateral and bilateral elements.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… Network Analysis Lab Manual

54

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 2. Does transformer networks with linear elements are reciprocal? If yes give a supporting example. If no, give a contradictory example.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… 3. Draw any non-reciprocal network in the space below.


55

Experiment No. 13 NETWORK ANALYSIS USING PSPICE OBJECTIVE To learn DC analysis, AC analysis and transient analysis of electrical networks u sing PSpice.

BACKGROUND 1. SPICE stands for Simulation Program with Integrated Circuit Emphasis 2. SPICE was originally developed at the Electronics Research Laboratory of the University of California, Berkeley (1975). As the name implies, SPICE was originally developed for designing integrated circuits. However, it can be used to analyze discrete circuits as well. 3. PSpice is a PC version of SPICE (Cadence) and HSpice is a version that runs on workstations and larger computers. 4. PSpice is case insensitive i.e. typing „r‟ or „R‟ will not be any different in PSpice. 5. All analysis can be done at different temperatures. The default temperature is 27˚c. 6. PSpice can do several types of circuit analysis. Here are a few:     

DC analysis: Calculates the DC transfer curve. AC analysis: Calculates the output as a function of frequency. A bode plot is generated. Transient analysis: Calculates the voltage and current as a function of time when a large signal is applied. Noise analysis: Analyzes noise at the input or output of the circuit. Fourier analysis: Calculates and plots the frequency spectrum.

7. A PSpice circuit can contain components like:        

AC & DC voltage and current sources Resistors and Variable Resistors Capacitors and Variable Capacitors Inductors and Variable Inductors Operational amplifiers Switches Diodes Bipolar transistors


56



Transformers etc

Getting started with PSpice

Go to “Start Menu”, then “Programs”, then “PSpice Student” and then “Schematics ”

The following schematic editor window will appear:


57

Drawing the Circuit Following is the circuit we will use to begin our understanding about how PSpice works:

A. Getting the Parts 



The first thing is to get some or all of the parts you need and place them on your

„Schematics Workspace‟. This can be done by o

o o





Going to "Draw" and selecting "Get New Part...", or Clicking on the 'get new parts' button Pressing "Control+G"

, or

Once this box is open, select a part that you want in your circuit. This can be done by typing in the „Part Name‟ or the first alphabet of the part name, or scrolling down the list until you find it.

Upon selecting your parts, click on the „Place‟ button. Then click where you want it to be placed on the schematics workspace. Don't worry about putting it in exactly the right place, it can always be moved later.


58



Once you have all the parts you think you need, close that box. You can always open it again later if you need more parts.

Get Recent Part Bin: PSpice keeps track of the most recent parts used and lists them in the Get Recent Part bin. You can save time by selecting items from this bin. Simply double click the item then place as described above.

B. Libraries in PSpice 

The parts in PSpice are arranged in the form of libraries. You do not have to worry about including the concerned libraries before you actually select Parts because PSpice

Schematics Version 9.1 automatically includes all the libraries, when the “Get Part” 

button is pressed. Few common libraries are:   

analog.slb: Contains resistors (R), capacitors (C), inductors (L), dependent sources (E, F,

G and H) etc.

source.slb: Contains various independent voltage and current sources. port.slb: contains elements such as ground etc.

Hands on Exercise 1  

Get all the parts you need to draw the circuit given, on your Schematics workspace? Find out what specific libraries contain those parts?


59

C. Placing the Parts     

You should have most of the parts available in your schematics workspace that you need at this point. To put them in the places that make the most sense (usually a rectangle works well for simple circuits), just select the part and drag it where you want it. To rotate parts so that they will fit in your circuit nicely, click on the part and click Edit simply click "Ctrl+R" To flip them, click Edit





"Rotate" or

"Flip" or "Ctrl+F".

If any parts are left over, just select them and press "Delete".

Hands on Exercise 2 

Place the parts that you have selected in Exercise 1 in a proper order on the Schematics workspace?

D. Connecting the Circuit 

Now that your parts are arranged well, you'll have to connect them with wires.



Go up to the tool bar and o

o o



Go to "Draw" and select "Wire", or Select "Draw Wire" Click "Ctrl+W"

, or

With the pencil looking pointer, left click on one end of a part. When you move your mouse around, you should see dotted lines appear. Drag the mouse to the next part in the circuit. This will attach the other end of the wire to the next part that you want to connect and then left click again to release the wire



Repeat this until your circuit is completely wired.



If you want to make a node (to make a wire go more than one place), click somewhere on the wire and then click to the part (or the other wire). Or you can go from the part to the wire. To get rid of the pencil, Right Click on the mouse.

 

If you end up with extra dots near your parts, you probably have an extra wire, select this short wire (it will turn red), then press "Delete".



If the wire doesn't look the way you want, you can make extra bends in it by clicking in different places on the way (each click will form a corner).


Connect the parts using the wire that you have placed in Exercise 2.


60

E. Changing the Name of the Part 

You probably don't want to keep the names R 1, R 2 etc., especially if you didn't put the parts in the most logical order. To change the name, double click on the present name (C1, or R1 or whatever your part is), then a box will pop up (Edit Reference Designator). In the top window, you can type in the name for the selected part.



Please note that if you double click on the part or its value, a different box will appear.


Change the names for the parts in your circuit to the names that were shown in the original figure of the circuit given.

F. Changing the Value of the Part 

To change the value of the part (e.g. by default the value of all the resistors is 1K ohms), you can double click on the present value and a box called "Set Attribute Value" will appear. Type in the new value and press OK.



If you double click on the part itself, you can select VALUE and change it in this box.


61



The list of units as PSpice accepts them is as follows:

F,f

femto

10-15

P,p

pico

10-12

N,n

nano

10-9

U,u

micro

10-6

M,m

milli

10-3

K,k

kilo

103

MEG,meg

mega

106

G,g

giga

109

T,t

tera

1012

Hands on Exercise 5 Change the values for the parts in your circuit to the values that were shown in the original circuit given.

G. Saving



If you have not done so, now is a good time to save your schematic. Choose a name that will help you identify which problem this is. To save the circuit, click on the save button on the tool bar (or any other way you normally save files).

H. Electric Rule Check Perform an electrical rules check to be sure your circuit schematic will simulate properly. (Analysis menu, Electrical Rule Check ). If all goes well, you will see a small window flash


62

on the screen and nothing else. If no errors are reported in your schematic, proceed to the next step. If there are errors, fix them now.


63


Do the Electrical Rule Check and Save the circuit that you have drawn?

I. Simulating the Circuit    

 

Now you will simulate your circuit. Do this by going to the Analysis menu and choosing Simulate or Press on the Toolbar. When simulation is done, a new PSPICE window will appear. Look at the Lower Left corner of the window for the results of simulation. This is what you are going to see:

What does PSpice mean by Floating Nodes? Why was the Simulation Aborted?

J. Making Sure You Have a GND 

This is very important. You cannot do any simulation on the circuit if you don't have a ground. If you aren't sure where to put it, place it near the negative side of your voltage source.

K. Reading the Output    

Select View in this window, and examine Output File. Scroll down towards the bottom of the file until you come to a series of headings that say Node Voltage. The voltage at each circuit node should be reported. Identify which node voltages are associated with which circuit elements and note them down. Scroll further down the output file. Note that the source current and total power dissipation for the circuit is also reported. The voltage source current is reported as -2.500E-04 A.


64


Find out the value of the current in the circuit manually by using the analytical methods you have

learned in the BEE class so far. Check if the answer agrees with PSpice‟s?

L. Netlists  

The netlist contains description of the circuit that describes the parts of the circuit and the nodes with which they are connected.





  

A netlist is the original way we interacted with SPICE.

When PSpice creates a circuit description from your schematic, it numbers nodes, and for each component, lists the nodes to which it is connected as well as the value of the component. For example, Node 1 is designated $N001, node 2 as $N002, etc.

These designations do not appear on your schematic screen but instead they reside in a file as a

“netlist”.

To view the netlist, click Analysis, then Examine Netlist.

In the netlist, the “1” end of a component is connected to the first indicated node.


Examine the Netlist for your circuit and compare these node numbers with the circuit you have drawn.

M. PSpice File Extensions PSpice file extension

Description

.SCH

Schematics diagram file.

.CIR

Control file generated by Schematics. ASCII.

.NET

Netlist (circuit description) generated by Schematics. ASCII.

.ALS

Alias file generated by Schematics. Needed for PSpice simulation.

.PRB

Control file for Probe plots. Contains settings from last run, scaling, etc.

.DAT

Complete output file generated by PSpice; input to Probe. Not readable; Normally a large file

.OUT

Readable ASCII output file from PSpice simulation.


65

Contains dc levels, etc.

N. Shortcut to find Bias Voltage and Current from the Toolbar 

You can use the ‘Enable Bias Voltage Display’

or „ Enable bias current display‟

buttons on the Schematics workspace toolbar to find out the Bias Voltage and Currents directly instead of reading them down from the output file.


Find out the bias voltages and currents for the circuit you have drawn using the above said buttons on the Schematic Window Toolbar.

O. Printing 

To print your schematic circuit, you must first use your mouse to make a rectangle around your circuit; this is the area of the page that will be printed. Then select print as usual. (You can select ).

P. Meter Elements IPRINT, VPRINT1 and VPRINT2 These are general purpose metering components that you can use to measure voltage and current. To determine their readings, you must examine the output file. (Click Analysis, Examine Output, then scroll until you find them.) Note that IPRINT and VPRINT1 have a terminal marked with a „ „sign that corresponds to the COM terminal on a real physical meter. You must wire them into your circuit as you would a real meter, taking into account where you want the COM terminal. In addition, you must configure them for the type of measurement (dc or ac) that you wish to make.


66

Hands on Exercise 10 Place the above mentioned metering elements in the circuit below and show the results.

Q. Dependent Sources

Voltage controlled voltage source

Current-controlled current source

Voltage controlled current source

Current-controlled voltage source

A controlled voltage source is one whose output voltage is controlled by (depends on) the value of a voltage or current elsewhere in the circuit. A current controlled voltage source obeys the relation vo=ki, where „i‟ is the controlling current and k is a constant having the units of resistance: k=vo/i volts per ampere, or ohms. Similarly, a controlled current source produces a current whose value depends on a voltage or a current elsewhere in the circuit. A voltage-controlled current source obeys the relation io=kv, where v is the controlling voltage and k has the units of conductance: k=io/v amperes per volt, or siemens. All four types of controlled sources, voltage-controlled voltage source, current-controlled voltage sources, voltage-controlled current sources, and current-controlled current sources, can be modeled in PSpice. Network Analysis Lab Manual

67

Hands on Exercise 11

The circuit shown in Figure below has a current controlled voltage source with the gain of „3‟.

This circuit can be constructed in PSpice using part “H” as shown in figure below:

Click the part and enter gain =3. Save and simulate it.

Learn to perform ac analysis and transient analysis using PSpice Setting-up Analysis 

  

You can select and specify a PSpice analysis.

To add up analysis, select set up to display „analysis setup‟ dialog box, or click the button. You can make your required selections from here. When you are done, select the check boxes of the analysis you want to use. Click the close button.


68

Bias Point Detail Bias Point Detail writes the detailed bias information to the simulation o utput file. The information reported to the output file includes: (i) Node voltages (ii) Current through Voltage sources (iii) Total power

DC Sweep 

The DC analysis causes a dc sweep to be performed. The dc sweep analysis calculates the

circuit‟s bias point over a range of values.  

The DC sweep allows you to do various different sweeps of your circuit to see how it responds to various conditions. For all the possible sweeps,

voltage, current, o temperature, and o model and global parameter o o

 

You need to specify a start value, an end value, and the number of points you wish to calculate. For example you can sweep your circuit over a voltage range fr om 0 to 12 volts. The main two sweeps that will be most important to us at this stage are the voltage sweep

and the current sweep. For these two, you need to indicate to PSpice the component name you wish to sweep, for example V1 or V2. Voltage and Current Markers 



These are important if you want to trace the voltage at a point or the current going through that point.

To add voltage or current Marker, go to the top tool bar and select „Voltage/Level Marker‟ or „Current Marker‟ or press „Ctrl+M‟. Also you can go to „Markers‟ on tool bar and select either „Mark Voltage Level‟ or „Mark current into pin‟.


69

Probe     



  



(a) Before you do the Probe You have to have your circuit properly drawn and saved. There must not be any floating parts on your workspace (i.e. unattached devices). You should make sure that all parts have the values that you want. There are no extra wires. It is very important that you have a ground on your circuit.

Make sure that you have done the enabled. (b) To Start the Probe

Analysis Setup and specify the values you want

Click on the Simulate button on the tool bar

(or Analysis, Simulate, or F11).

It will check to make sure you don't have any errors. If you do have errors, correct them. Then a new window will pop up. Here is where you can do your graphs. (c) Adding/Deleting Traces

If you‟ve placed the voltage/current level markers, PSpice will automatically put the related traces in. You can change them or add to them.





Go to „Trace‟, then „Add Trace‟ or click

on the toolbar. Then select all the traces you want. Do not forget to add a new Y-axis if the two plots have different yaxis scaling.

To delete traces, select them on the bottom of the graph and press „Delete‟ button from

keyboard. (d) Doing Math   

   

In Add Traces, there are various mathematical functions that can be performed. These will add/subtract (or whatever you chose) the traces together. Select the first output then click the function that you wish to perform. There are many functions here that may or may not be useful. If you want to know how to use them, you can use PSpice's Help Menu. (e) Labeling

Click on „Text Label‟

on top tool bar.

Type in what you want to write. Click OK You can move this around on your graph by single clicking and dragging.

(f) Finding Points 



There are Cursor buttons that allow you to find the maximum, minimum or just any point on the line. These are located on the right side of the toolbar.

Select which curve you want to look at and then select „Toggle Cursor‟


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(g) Saving 

To save your probe you need to go into the tools menu and click „Window‟. Now click „display control‟. This will open up a menu, which will allow you to name the probe file and choose where to save it. You can open previously saved plots from here as well. (h) Printing

 

Select „Print‟ in „File‟ menu or click

on the toolbar.

Print as usual.

Another excellent feature of the DC sweep in PSpice is the ability to do a nested sweep. A nested sweep allows you to run two simultaneous sweeps to see how changes in two different DC sources will affect your circuit.

Example 1 For the following circuit we will dc sweep the voltage source from 0V to 10V and observe the trace of VR1 and VR2.

  

 

      



Draw the circuit in your schematic workspace. Label the nodes „a‟ and „b‟ as shown in the diagram above. Go to „Analysis‟, then „setup‟ and select „DC Sweep‟ from the dialog box.

„Sweep var. Type‟ is set to voltage source by default. We are providing dc sweep to voltage source so we will not change it.

Write the name of voltage source i.e. „V1‟ in place of „Name‟. Enter start and end values i.e. 0 and 10 and give any convenient value of increment e.g. 1.

Leave the „Sweep Type‟ set to its default value i.e. „linear‟. Place a voltage level marker at node „b‟. Save and simulate your circuit. A new probe window will open with the trace of voltage across R2.

To add the trace of voltage across R1, go to Trace menu and click ‟Add Trace‟. Enter trace expression „V (a) - V (b)‟ and enter.

You can observe that at each point sum of both voltages is equal to the value of V1. Hence Kirchhoff‟s voltage law is prove d.


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Also add the trace of current through R 1. If the current trace turns out to be zero, find out the parameter that needs to be adjusted.

Example 2 Prove maximum power transfer theorem using global variable dc sweep

This circuit models a source (V S , RS ) and a load R L. The problem is that the source is given, and we want to determine the value of R L for which the power absorbed by the load PL = (VL)2/R L is a maximum. We will simulate and obtain a graph of P L versus R L, and determine the value of R L at maximum value of P L  

      

  

 

Draw the circuit on your schematics workspace.

From „Get New Part‟ place „PARAM‟ anywhere on your workspace.

Double click on the part PARAM after placing on the schematic workspace and set

„NAME1‟ to „RL_val‟ and „VALUE 1‟ to be equal to‟1‟.

Go to ANALYSIS and then SETUP and click on DC SWEEP. In the SWEPT VARIABLE TYPE select GLOBAL PARAMETER. Write the NAME as RL_val. This will be the swept variable. Set the SWEEP TYPE to OCTAVE. Set START VALUE to 10, END VALUE to 100k and INCREMENT to 10. Save and simulate.

Do not forget to change the attribute value of RL to RL_val enclosed in curly brackets. On the display window, go to TRACE and then ADD TRACE. In the ADD TRACE window, enter the following expression (-VL x I(RL)).

Find out the value of RL for which the power is maximum. Also find out the value of the maximum PL that is transferred. This must verify the maximum power transfer theorem, which states that maximum power is transferred from source to load when R L = RS

Exercise For the given circuit trace the voltage across R 2 by sweeping dc current source from 0 to 10 Amp. Also on the probe mark points at VR2 for I1=5 Amp.


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Transient Analysis 



In transient analysis, we determine voltages and currents as function of time. Typically time dependence is demonstrated by plotting the waveforms using time as independent variable. Two very important parameters in the transient analysis are: o

o

print step: It s pecifies time interval used for printing and plotting the results of transient analysis. It refers only to results written to output file. It has no effect on probe data file. final time: This specifies ending time for which the cir cuit‟s behavior is calculated.

Example Draw the following circuit in PSpice

    





Open the attribute window for the capacitor and set IC=0. after changing them.

Don‟t forget to save the attributes

Place a Voltage Marker at node vout to find out the voltage across it. Run the probe. Add the trace for Vout i.e. the voltage across the capacitor.

Above results can be achieved by using „VPULSE‟ in place of „VDC‟ as shown:

Exercise Trace the current through the capacitor in the above circuit.

Observe the behavior of inductors for dc circuits by setting the IC for inductor equal to 0A.


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D) AC Sweep 

Ac steady state analysis is facilitated by the use of phasors. PSpice can perform ac steady state simulation, outputting magnitude and phase data for any voltage or current of interest at any frequency.



Additionally PSpice can perform an ac sweep in which the frequency of sinusoidal sources is varied over a user-defined range. In this case simulation results are the magnitude and phase of every node voltage and branch current as a function of frequency.



In the AC sweep menu you have the choice of three AC sweep types: o o o



Linear Octave Decade.

These three choices describe the x-axis scaling of the trace. For example, if you choose decade then the scale of x-axis will be logarithmic i.e. 10Hz, 1 kHz, 100 kHz, 10 MHz, etc. Decade option is used to see the behavior of any circuit over large range of frequencies.



You now have to specify at how many points you want PSpice to calculate results, and what the start and end frequency will be. That is, you choose range of frequencies to simulate your circuit.



In the AC sweep you also have the option of Noise enable in which PSpice will simulate noise for you either on the output or the input of the circuit. These noise calculations are performed at each frequency step and can be plotted in probe.

Example 

Simulate the given circuit at a frequency of 60 Hz.

Single Frequency AC Simulation  





Draw the circuit in your schematics workspace. The AC source, VAC , is in the source library. To set up the AC source for simulation, double click on the source symbol and open its ATTRIBUTES box.

The DC attribute is the dc value of the source for dc analyses. The ACMAG and ACPHASE attributes set the magnitude and phase of the phasor representing V in for ac analysis. To specify the frequency for simulation, select Setup from the Analysis menu and go to AC sweep.


74



Set all fields for 60-Hz simulation as shown in the figure below:



Since simulation is performed at only on frequency, 60 Hz, graphing the simulation results is not a very attractive option. So to write the magnitude and phase of the phasor Vout to output file, use VPRINT1 part from SPECIAL library as shown below:







After placing VPRINT1 part and set its attributes. The VPRINT1 part can be configured to meter the node voltage in any kind of simulation: dc, ac, or transient. Since an ac analysis is specified in the setup, the values of AC, MAG, and PHASE attributes are set to Y, where Y stands for yes. When an AC sweep is performed, PSpice, unless instructed otherwise will attempt to plot the results using the probe plotting program. To turn off this feature, select Probe Setup in the Analysis menu and select Do Not Auto-Run Probe. Simulate the circuit and select Examine Output from the Analysis menu to view the data. At the bottom of the file we will find the desired results.

Exercise 

Simulate the above circuit at a frequency of 50 Hz to find the current through the circuit using IPRINT part and display the results in the output file.

Variable Frequency Ac Simulation 

To sweep the frequency over a range, 1 Hz to 10 MHz, for example, return to AC SWEEP AND NOISE ANALYSIS box. Change the fields to the desired values as shown below:


75

 



 

Since the frequency range is so large, choose a log axis for frequency with 50 data points in each decade We can now plot the data using probe utility. This procedure requires two steps. First, remove VPRINT1 part. Second, return to PROBE SETUP window and select

„ Automatically Run Probe After Simulation‟. Save and simulate the circuit.

To plot magnitude and phase of V out on the probe window, select Add from the trace menu. For magnitude of Vout, select V (Vout) and click OK. Before plotting phase, select Add Y axis from Plot menu. Now go to add traces and add the expression P (Vout). Click OK.

Exercise 

Also plot the magnitude and phase of current through the capacitor in the above circuit over a frequency range of 100 Hz to 600 kHz.

E) Parametric Sweep  







One of the more useful aspects of SPICE is the ability to run a number of variations on a basic circuit and compare the results by plotting them on the same graph. For our example it might be interesting to see how changing the resistor value affects the frequency response and make comparison with the first simulation.

A hard-nosed way of doing that might be to select the circuit, make a copy, start a new project with all of the same settings, paste the circuit into the new project, make the desired parameter changes, run the simulation, and then add the new trace to the old graph. This might seem like a lot of goofing around, but indeed there is a simpler approach.

Instead, you can use the parameter sweep feature of spice. A parameter sweep allows you to specify a number of values for a particular parameter and then perform a complete analysis for each value.

Example Draw the following circuit:


76

  

     

    



Double-click on the resistor value and change its value from 10k to {RA}. (Make sure that you are changing the value and not the name.) The curly brackets are important. Go to the ANALYSIS menu and choose SETUP. Now choose PARAMETRIC.

In the new window, under the SWEPT Var. TYPE, select GLOBAL PARAMETER and in the "Parameter name" entry box type in RA In the "Sweep Type" section, you could enter start, stop, and increment values for R1. Since we want only a few values, we will use a VALUE LIST option on the LHS menu. Click the button next to "Value List" and enter 1k 10k 100k (no commas separating the values). Thus, we are planning to run the simulation 3 times with those three values for R1. Click OK.

We need to add one more part to the schematic so that PSPICE can handle the parameter sweep properly. Go to GET PART and select the part named PARAM. Place it any where on the schematic workspace. Double-click on the "Parameters:" part to bring up the "Property Editor" window. Type RA for NAME 1 and 1k for VALUE 1.This shows that 1k will be the first value used in the parameter sweep. Finally, click on CHANGE DISPLAY and select BOTH NAME and VALUE. You should see the schematic workspace that is something like the one below:

Set the AC sweep settings over a range of frequencies 10 Hz to 100 kHz and

10pts/decade (Don‟t forget to select decade in the ac sweep type). Now Simulate your circuit.


77



 

Assuming there are no errors, when the simulation is finished, you should see a message saying that three separate files are available. You can choose any or all of them for plotting. In this case choose "All" and click OK. From the TRACE menu choose ADD TRACE in the dialog, choose "DB( )" from the math function list and then choose V(Vout) from the circuit variables list. Click OK and a graph will appear, showing three different frequency responses for the three different values of resistor.

F) Sensitivity  

Sensitivity causes a DC sensitivity analysis to be performed in which one or more output variables may be specified. Device sensitivities are provided for the following device types only: resistors, o o o o o





independent voltage and current sources, voltage and current-controlled switches, diodes, and bipolar transistors.

You would use the sensitivity settings for discovering the maximum range of circuit performance and the causes of extreme operation. These techniques are used to identify effective changes to improve the quality of circuit operation. This isn't as important for us in the lab, but some day when you are constructing real circuits that need to function under various conditions this will be useful.

G) Temperature 



The temperature option allows you to specify a temperature, or a list of temperatures (do not include commas between temperature values) for which PSpice will simulate your circuit. For a list of temperatures that simulation is done for each specified temperature.

H) Digital Setup 

 



In addition to letting you simulate analog circuits, PSpice provides a number of digital parts that can be used in a homogeneous digital circuit, or a heterogeneous analog/digital combination. The digital analysis option allows you to specify the timing of your circuit, by running the gates at their minimum, maximum and typical values. A superb feature allows you to test the worst-case timing of your circuit to see how it will operate under these extreme conditions.

You also have the option of setting the value of any flip flops you have in your circuit to predefined states which is good to simulate any startup conditions for finite state machines that you are simulating.


78

DISCUSSION 1. What are the powers of PSpice those you have explored in this lab?

………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………………………………………


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Experiment No. 14 ELECTRICAL NETWORK MODELING IN MATLAB SYMBOLIC TOOLBOX OBJECTIVE To learn modeling of electrical networks in frequency domain using Matlab symbolic toolbox.

THEORY Consult MATLAB documentation to get help for each of the following command(s) if you

don‟t understand.

EQUIPMENT Computer with Matlab & Simulink installation

PRACTICE The following example illustrates the difference the between a standard MATLAB data type, such as, double and the corresponding symbolic object. Example 1:- Enter the following commands and observe the difference. >> clear >> sqrt(7) >> a = sqrt ( sym(7)) >> 3/8 >> sym (3)/sym (8) >> 1/5+2/3 >> sym (1)/sym (5) +sym (2)/sym (3)

Example 2:- sym command lets us construct the symbolic variables and expressions as below; >>clear >> x = sym('x') >> a = sym('a') >> x = sym( '(1+sqrt(5))/2') >> f = x^2 – x -1


80

f =(1/2+1/2*5^(1/2))^2-3/2-1/2*5^(1/2)

The expression returned by f is complex to read. Enter the following command. >> simplify(f)

Example 3:- This example describes another way to declare the symbolic objects. >> clear >> syms a b c x

We may construct quadratic equation using above variables. >> f = sym ('a*x^2 + b*x + c')

Note: - To create a symbolic expression that is a constant, you must use the sym command. For example, to create the expression whose value is 5, enter f = sym ('5'). Note that the command f =5 does not define f as a symbolic expression. findsym informs about symbolic variable of an expression. >> findsym (f)

Observe the difference between the following commands. >> subs ( f, 2) >>subs(f, a, 2)

Example 4:- Example illustrates creation of real and complex variables. >> clear >>x = sym('x', 'real'); >>y = sym('y', 'real');

or more efficiently >>syms x y real >>z = x + i*y >> z*conj (z) >> simplify (z*conj (z))

Example 5: - Symbolic toolbox has the power to solve derivatives. Network Analysis Lab Manual

81

>> clear >> syms x >> h =sin(2*x) >> diff(h)

To take second derivative we use >> diff(h,2) or >> diff (diff (h))

Example 6: - Let us find derivative of functions having more than one variable. >>clear >>syms x y >> f = exp(x*y)

Observe the output of each of the following commands. >> diff (f) >> diff (f,x) >> diff (f,y) >>diff ( f,y,2) >> diff(f,2) Your Task ???

You have studied command for differentiation. Is there any command for integration? If yes, find the following and write those commands beside. 3

5tdt 1

Electrical Network Modeling in Frequency Domain Example 7:- Following example shows power of symbolic toolbox to calculate Laplace transform. (Make an M-file and having finished delete it). >> clear >> f =2*exp(-t) – 2*exp(-2*t) >> pretty(f) >> F = laplace(f) >> pretty(F) Network Analysis Lab Manual

82

>>simplify(F) >>pretty(F)

Example 8: - The inverse Laplace transform is also possible to calculate. >> clear >> syms s >> F = 2 / [(s+1)*(s+2)]; >>pretty(F) >> f = ilaplace (F) >> pretty (f)

Example 9:- In the following example, we use Cramer Rule to solve following circuit in Symbolic toolbox.

I1

I2

Figure 1: Electrical Network

In Laplace domain loop equations become; (sL + R)I 1 – R I2 -RI1 + (1/sC+R)I2

Ls

R

R 1 sC

R

R

= Vin = 0

V

I 1

in

I 2

0

Using Cramer Rule we find R 1 0 R sC R R 1 R R sC in

I 1

Ls

and


83

Ls R 2

R Ls R R

R

Vin

0 R 1 sC

Where I1 is current in first loop and I2 is current in second loop. Following is the code to solve the circuit using Symbolic toolbox. >> syms Vin L R C s >> A = [s*L+R

-R ; -R (1/(s*C))+R];

>> A1 = [Vin -R ; 0

( R+1/(s*C))];

>> I1 = det(A1) / det(A); >> simplify (I1)

Similarly find I2 in s domain.

RESULTS For the above network the time domain solution for the loop currents will be i1(t)=…………………………….. i2(t)=……………………………..

DISCUSSION 1. Find Laplace transform of the following time functions manually and by using Matlab commands;

a) f

5t 2 cos(3t 45)

b) f

5t e 2t sin(4t 60)

2.

a)

Find inverse laplace of the following functions using Matlab commands. 1000

s3 40 s 2 300 s b).

s

2

s( s

2

6 s

5

4 s

5)


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3. What you have learnt in this lab?

………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… 4. Plot the following functions using Matlab commands. Draw the sketches and write

commands in space below. (See Matlab help…..)

a) i(t ) 5cos(3t ) b) i(t ) 3e 2t sin t


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Experiment No. 15 TWO PORT PARAMETERS OBJECTIVE To determine two port network z parameters. To determine two port network y parameters.

THEORY A general two port network is shown in Figure 1. The Z parameters are also known as open circuit impedance parameters. The Z parameters of a two port network are Z 11, Z 12, Z 21 and Z22 and these are given by Z11 = V1/I1 when I2 = 0 i.e. secondary is open circuited. Z12 = V1/I2 when 11 = 0 i.e. primary is open circuited. Z21 = V2/I1 when I2 = 0 i.e. secondary is open circuited. Z22 = V2/I2 when I1 =0 i.e. primary is open circuited.

Figure 1: A Two Port Network

The Y parameters are also known as short circuit admittance parameters. The Y parameters of a two port network are Y11, Y12, Y21 and Y22 and these are given by Y11 = I1/V1 when V2 = 0 i.e. secondary is short circuited. Y12 = I1 /V2 when V1 = 0 i.e. primary is short circuited. Y21 = I2/V1 when V2 = 0 i.e. secondary is short circuited. Y22 = I2/V2 when V1 =0 i.e. primary is short circuited.

EQUIPMENT DC power supply


Digital multimeter

86

Jumpers wires

Resistors: 1kΩ (2), 2.2 kΩ, 1Ω(2)

Breadboard

CIRCUIT DIAGRAM

Figure 2: For Z11 and Z21 where I2=0

Figure 3: For Z12 and Z22 where I1=0

Figure 4: For Y 11 and Y 21 where V2=0


87

Figure 5: For Y12 and Y 22 where V1=0

PROCEDURE Connect the components on bread board according the circuit diagram of Figure 2. Observe and note values of V1, V2 and I1 by using oscilloscope or multimeter. Find Z11 and Z21. Now connect the components on bread board according the circuit diagram of Figure 3. 5. Observe and note values of V1, V2 and I2 by using oscilloscope or multimeter. 6. Find Z12 and Z22. 7. Connect the components on bread board according the circuit diagram of Figure 4. 8. Observe and note values of V1, I2 and I1 by using oscilloscope or multimeter. 9. Find Y11 and Y21. 10. Now connect the components on bread board according the circuit diagram of Figure 5. 11. Observe and note values of I1, V2 and I2 by using oscilloscope or multimeter. 12. Find Y12 and Y22. 1. 2. 3. 4.

RESULTS For Figure 2,

For Figure 4,

V1=

V1=

V2 =

I2=

I1= Z11 = V1/I1 =

I1= Y11= I1/V1=

Z21= V2/I1 =

Y21= I2/V1=

For Figure 3,

For Figure 5,

V1=

I1=

V2=

V2 =

I2 = Z12= V1/I2 =

I2= Y12= I1/V2=

Z22 = V2/I2 =

Y22= I2/V2=

DISCUSSION 1. Find impedance and admittance parameters theoretically and compare the values with practical results.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… Network Analysis Lab Manual

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NEtwork Analysis Lab Manual

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