laboratory manual - gazi Üniversitesiw3.gazi.edu.tr/~mtozden/em212_lab_foyu_2011-2012.pdf · gazi...

GAZI UNIVERSITY

FACULTY OF ENGINEERING

DEPARTMENT OF

ELECTRICAL AND ELECTRONICS ENGINEERING

EM 212

INTRODUCTION TO ELECTRONICS

LABORATORY MANUAL

2011-2012 SPRING

EM212 Introduction to Electronics Lab. 2011-2012 Spring 1

TABLE OF CONTENTS

Page

LABORATORY RULES .................................................................................................................................................... 2

EXP# 1 - CHARACTERISTICS OF DIODES, DIODE MODELING .............................................................................. 3

EXP# 2 - DIODE CIRCUITS ............................................................................................................................................. 5

EXP# 3 - DIODE APPLICATIONS (RECTIFIER CIRCUITS) ........................................................................................ 7

EXP# 4 - ZENER DIODE APPLICATIONS ..................................................................................................................... 9

EXP# 5 – CHARACTERISTICS OF BJT .......................................................................................................................... 9

EXP# 6 - POLARIZATION AND THERMAL CHANGE IN TRANSISTORS ............................................................. 13

EXP# 7 - DC and AC ANALYSIS ON TRANSISTORS ................................................................................................. 15

EXP# 8 - THE CHARACTERISTICS OF JFET and JFET AS A VOLTAGE-CONTROLLED RESISTOR................. 17

EXP# 9 - JFET DC and AC ANALYSIS ......................................................................................................................... 19

Laboratory Schedule

Experiment Date

Experiment 1 12-16 March



Experiment 4 2-6 April



Experiment 7 23-27April

Experiment 8 30 April -4 May

Experiment 9 (Pspice Application) 7-11 May


Gazi University

Department of Electrical and Electronics Engineering

EM212 Introduction to Electronics Lab.

LABORATORY RULES

Attendance

There will be NO make-up experiment.

Students who cannot attend an experiment get zero from the preliminary work, report, quiz and performance of that experiment.

Students who miss 2 or more experiment fail from the laboratory and cannot attend to the final exam of EM 212 course.

There will be a pop-up quiz at the first 15 minutes of your laboratory session. If you come to class during a quiz, you can attend to that quiz with remaining time. Students who come after the end of quiz, cannot have the quiz and will not be accepted to the experiment.

Experiment Reports

Reports are prepared by the experiment group. Group members do not present personal reports.

Each member of the group gets the same degree from the report.

Reports are delivered at the next experiment.

During the experiment;

Use a grounded power for signal generator and non-grounded power for oscilloscope

Always connect DC supply first and than AC supply. At the end, disconnect AC supply and than DC supply.

Before beginning the measurements, check the calibration of your oscilloscope.

After the experiment, turn off all the equipments and clean your tables.

Always use electrical quantities like voltage or ampere on your result sheet.

If there is a problem about your equipments, consult the instructors before replacing it.

Degrees

You will have a performance degree at the end of each experiment according to your working discipline, interest on the laboratory, success on the experiment and etc.

At the end of the term, your final laboratory degree will be calculated as follows; Final Lab. Degree: 30% Reports 15% Quizzes 15% Performance 40% Lab. Final Exam


Gazi University



EXP# 1 - CHARACTERISTICS OF DIODES, DIODE MODELING

PURPOSE: In this experiment, the i-v characteristics of the silicon, germanium, zener diodes and LED’s will be investigated and diode voltages and resistances will be calculated. Rather than plotting the i-v curve point by point, an AC signal will be used to display the i-v characteristics on CRO.

EXPERIMENTAL PROCEDURE:

1. Testing Diodes: The AVO (Ohmmeter) Method: A quick way of determining whether a diode is defective or not is to use an ohmmeter. If the internal battery of the ohmmeter forward biases the pn junction, a low resistance is read on the scale. Otherwise a high resistance is read. If the diode is defective, the ratio of the two readings is close to unity (poor rectification). a) Using the AVO meter, test your diodes. b) Determine their anodes. Does the band on the diode indicate the cathode or the anode terminal?

2. Determining Diode Voltages (Vγ): Set up the circuit in Figure 1. At first, set the variable DC source to 0 Volt. Then slowly increase its value, while watching the input voltage and the voltage on the diode from the scope. Using this circuit, how could you find the forward biasing voltage (Vγ) of the diodes?. Determine this value for four different (Si, Ge, Zener, LED) diodes.

Y150

X

R

W

D

Figure 1

3. Characteristic of Diode: Set up the following circuit to display the i-v characteristics of four different -Si, Ge, Zener, LED- diodes. Vi(t)=4 Sin wt, f=200 Hz

Y

150S.G.

X

R W

D

Figure. 2


a) Set both channels to DC. Set the scope into X-Y mode. b) Obtain i-v characteristic of the diode and draw it by scale.

Calculate rf , Vγ, values from the curve and write them on following table.

c) Repeat the same process for Zener diode. Calculate rf , Vγ, Vz, rz values and write them on the table.

Can you observe the zener region with an input signal of Vi(t)=4 Sin wt ? If the answer is no, why and what do you suggest for doing this?

R=150 W

DIODES rf V rz Vz

1N4001 ( Si ) XXXXXX XXXXXX

Ge Diode XXXXXX XXXXXX

4.7 V Zener

LED XXXXXX XXXXXX

Table 1

RESULTS AND CONCLUSIONS 1. For which purpose do we use diodes ? 2. Why are the conduction voltage and zener voltage of each diode different ? 2. AC power supply was used to obtain the i-v characteristics of diodes. Why ? Can this process be done

with DC power supply ?

EQUIPMENT LIST PART LIST Oscilloscope 1N4001 (Si) diode Signal generator Ge diode Power supply 4.7 V zener diode Red LED 150 Ω,


Gazi University



EXP# 2 - DIODE CIRCUITS

PURPOSE: Two diode application circuits, Clipper and Clamper circuits will be designed and performance of these will be investigated experimentally in the laboratory.

PRELIMINARY WORK: Design the circuits that have the following characteristic by using ideal diodes, resistors and batteries.

1

1

2

V (volt)

i (mA)

1,5

Figure 1

1. Clipper (Limiter) with Diode a) Set up the circuit shown Fig.2. Apply a sinusoidal wave with an amplitude of 10 V to the input and obtain

its transfer characteristic on oscilloscope screen and draw it on paper. b) Repeat (a) for triangle and square waves with 10 V peak values. c) While a sine wave is applied to input, lower the dc voltage levels (V1 and V2) and observe that the output

waveform looks like a square wave. Vi(t)=10Sin wt, f=100 Hz

S.G.10 sin wt

100 Hz

1 K

X

Y

V1=3 V V

2= 6 V

D1 D2

+

+

-

-

Figure 2

2. Clamper Circuit Set channel 1 or channel 2 to DC. Vi(t)=8Sin(ωt) , f=100 Hz , V

DC = 3V

a) Set up the circuit shown in Fig.3 and for RL=1 KΩ, 100KΩ draw its output waveforms for sine, triangle and square waves. Observe the clamper voltage to be V

DC + Vγ.

b) Adjust Vdc to zero volt. Set the load resistance values to RL = 100 KΩ and draw the output waveforms for

each case.


8 sin wt

100 HzS.G.

+ - Vout

RL

Vdc

+

-

D1 μF

V

Figure 3

RESULTS AND CONCLUSIONS Explain the operation principles of Clipper circuits and Clamper circuits. Comment on the results you have obtained .

EQUIPMENT LIST PART LIST Oscilloscope 1N4001 (Si) diode (2 pieces) Signal generator 1 K, 100 K resistors Power supply 1 micro F capacitor


Gazi University



EXP# 3 - DIODE APPLICATIONS (RECTIFIER CIRCUITS)

PURPOSE: Some measurements and applications on half- wave rectifier and full -wave rectifier circuits set up with silicon diodes.

PRELIMINARY WORK:

1) At the bridge rectifier circuit, neglecting supply resistors and assuming that C is very big, show that the following formula is correct:

VDC = Vm - Tidc / 4C, ( >> T)

2) Explain how each circuit used in this experiment works. Also explain their functions and draw output versus input graphics.

EXPERIMENTAL PROCEDURE: AC-GND-DC commutator should be in the DC position. 1)

a) Set up the half-wave circuit in Figure 1. Plot the output and input waves on scale. (C is not connected to the circuit). Measure DC output value by DVM (digital voltmeter).

b) Connect a 10 μF capacitor to the output. Observe the change in the waveform and report it. c) Connect a 470 μF capacitor to the output. Observe the change in the waveform and report it.

2) Set up the full-wave rectifier circuit. Report the output and input waveforms. Observe about 1.5 V voltage difference between input and output voltages. Repeat process 1b for this circuit.

3) Set up the circuit in Figure 2b. Observe and record the output. Compare it with that of the circuit in Figure 2a.

220 V 6,3 Vrms

+ -

1 K+

-

10 μF, 470 μF

Vo

V

Figure 1

1 K 10 μF+

-

Vo

6,3 Vrms

220 V

1 K 10 μF+

-

Vo

6,3 Vrms

6,3 Vrms

220 V

Figure 2a Figure 2b


4) Set up the circuit in Figure 3 and record the output. (Repeat 4 for R=10 kΩ and R=100 kΩ)

220 V 6,3 Vrms 1 K

10 μF

D1

D2

Vo+ -

C1

C2

10 μF

Figure 3

RESULTS and CONCLUSIONS:

1) How much voltage difference is there between input and output of the bridge rectifier? What is the reason

for it? 2) What is the reason for the difference in the peak values of the consequent pulses of the output waveform

when the full-wave rectifier with a center-tapped transformer is used?

EQUIPMENT LIST PART LIST Oscilloscope 220V / 6.3V transformer DVM (AVO meter) 1N4001 diodes (4 pieces) 1 K, 10 K, 100 K resistors 10 μF capacitor (2 pieces) 470 μF capacitor


Gazi University



EXP# 4 - ZENER DIODE APPLICATIONS

PURPOSE: To observe the operation characteristics of zener diodes.

PRELIMINARY WORK: In Figure 1, let V=12 V and R=500 Ω. If RL is changed between 500 and 1000 Ω, what would be the maximum and minimum voltage at the output ( rz = 40 Ω, Vz=5 Volt)

R

+

-

V RL

+

-

Vo

iz

iL

Figure 1

EXPERIMENTAL PROCEDURE: AC-GND-DC commutator should be in the DC position.

A. Regulator with a zener diode

1)

a) Set up the circuit in Figure 2. Plot the signals at the points A and B.

b) Repeat (a) without the zener diode.

c) Remove the capacitor and observe and plot the waveform at the output. (Zener connected)

1 K220 μF

+

-6,3 V

rms220 V

270

4,7 V

W BA

Figure 2


B. Clipper (Limiter) Circuit

1) Set the circuit in Figure 3. Taking vin equal to 9 Sinwt (w=2000), observe and plot the output waveform. 2) Obtain the transfer function of the circuit.

470

4,7 V

S.G.

Vo

Vin

9 sin wt

W

4,7 VZ1

Z2

Figure 3

C. Level Shifter 1) Set the circuit in Figure 4. Adjust vin to be 8 + 2 sin ωt (ω=2000π).

2) Draw vin and vo waveforms.

4,7 VS.G.V

o

VZ

8 V+

-

+

-

470W

Figure 4

RESULTS AND CONCLUSIONS: 1) In clipper circuit, explain the function of the serially connected resistor between Vin and the zener diode. 2) In figure 4, how does adding one more zener diode affect voltage magnitude? 3) If VA = 4 V in the regulator circuit with a zener diode, how would the output signal be?

EQUIPMENT LIST PART LIST

Oscilloscope 1N4001 diode (4 pieces) Signal Generator 4.7 Volt zener diode (2 pieces) Power Supply 470 Ω resistor 270 Ω resistor 1 KΩ resistor 220 μF capacitor


Gazi University



EXP# 5 - CHARACTERISTICS OF BJT

PURPOSE: In this experiment, characteristics of BJTs will be investigated. Input and output characteristics of a common emitter connected BJT will be obtained.

PRELIMINARY WORK: Recalling that a transistor has two p-n junctions, explain how you can find out whether a transistor is good or out of order and which type it is. How do you understand its type by ohmmeter?

EXPERIMENTAL PROCEDURE: f=100 Hz

1) Set up the common emitter connected circuit shown in Figure 1. Obtain the ic - vce characteristic. a) Adjust the 1 M pot to its minimum (why?) and measure IBmax. b) Take two different IB values between IBmin -IBmax and plot the Ic - Vce curves.

BC 238,239

(npn)

1N4001 1 K

S.G.

150

1 M (pot)

47 K

12 V+

-

W

IB

10 sin wt

W

X

Y

BC

238

C EB

Figure 1 2) Set VCE=0 in the circuit of Figure 2. Obtain the transistor input characteristic. Repeat for VCE = 12 V.

(S.G=10 Sin wt, f=100 Hz)

W

X

10 K

S.G.

47BC 238 V

CE

+

-

Y

Figure 2


RESULTS AND CONCLUSIONS:

1) Explain the functions of the diodes used in the experiment.

2) Explain the function of the signal generator in the experiment.

3) What is the purpose of measuring the voltage across the 150 Ω resistor?

EQUIPMENT LIST PART LIST Oscilloscope 47 Ω, 150 Ω, Signal Generator 1 KΩ, 10 KΩ, 47 KΩ, DC Power Source 1 MΩ pot AVO meter BC238 (or BC548) (npn) 1N4001 diode


Gazi University



EXP# 6 - POLARIZATION AND THERMAL CHANGE IN TRANSISTORS

PURPOSE: To explain thermal changes of a BJT and analysis of its thermal stabilization.

PRELIMINARY WORK:

1) a) Compute R1 for Vcq to be 7 Volt in Figure 1. (Vbe = 0.6Volt, β = 80, Ico = 0)

R1

820

12 V

W

330

R1

470

12 V

W

W 330 47 K

R1

470

12 V

W

W

Figure 1

a) For every circuits, compute the stabilization factor, Se.

EXPERIMENTAL PROCEDURE: You do not need to use an oscilloscope in this experiment. An AVO meter is sufficient for all measurements.

1) Set up the circuit in Figure 2. For the R1 resistor you calculated, use the closest standard resistor. Measure IBQ, ICQ, VCEQ, VCQ.

BC 140

330

R1

470

12 V

W

W

180 K CB

E

BC140

Bottom

view

Metal case is

Collector

Figure 2


2) a) Set up the circuit in Figure 3. While the cooler is connected, adjust the C-E voltage to 6 volts. b) Unconnect the cooler and wait nearly for two minutes. By using a voltmeter, examine the voltage

change in C-E connection. c) Connect the cooler to the transistor again. Check the time for the voltage to reach its first value.

Record the last value of the voltage.

BC 140

470 K

(pot)150

+ 12 V

W

10 KBC 140

3310 K(pot)

10 K 150

+12 V

W

W

Figure 3 Figure 4

3) Set up the circuit in Figure 4 (above) and repeat the same processes as before.


1) Which is the most stable circuit among the ones used in the experiment. Why ?

2) What are the sources of changes in the stability factors in the circuits?

3) What is the function of a cooler ?

EQUIPMENT LIST PART LIST Power Supply BC140 transistor AVO meter 470 KΩ pot 10 KΩ pot 180 KΩ, 10 KΩ, 470 Ω, 330 Ω, 150 Ω, 33 Ω resistors


Gazi University



EXP# 7 - DC and AC ANALYSIS ON TRANSISTORS

PURPOSE: To determine operating points of transistors and to calculate their small signal parameters.

PRELIMINARY WORK: 1) For the circuit given in Figure 1, assume that VCEQ = 3.7 V, ICQ = 3.3 mA, stability constant Se = 37, Vbe

= 0.7 V, β = 100 ; a) Compute Rc, R1, R2. b) Plot the output characteristics for common emitter connected circuit on graph paper ( 0< Vbe < 20 ). c) Derive the equation of DC load line and plot it on the graph paper used in the previous step. Find cut

off and saturation points. d) Repeat (c) for AC conditions. e) What is the maximum peak to peak output voltage without any distortion. f) Draw the small signal model for the transistor; find rπ and β. g) Draw the small signal equivalent circuit and compute voltage gain, current gain, power gain and input

and output impedance values of the circuit. h) Compute CL and CS. Select the capacitances so that their reactance will be ten times as much the

equivalent resistance they see. 2) Experimentally, how do you find the input and output impedance of an amplifier? Suggest some methods.

VS (t)

1 K

CS

R1

R2

RC

680 ohmC

E

CL

470 ohm

+12 V

VL

Figure 1


1) Set up the circuit in Figure 2. Adjust R1 (470 K pot) so that VCE is half of VCC. (Don’t forget to disconnect the signal generator from the circuit )

2) Set the scope to ac mode. Connect the signal generator. Adjust the amplitude to a low level, where you obtain a distortion free output, and the frequency to 1 kHz. Then plot the vs(t) and vL(t) (set to scope dual mode) on the graph paper.

Set the scope dc mode. Plot vce(t), VCL (voltage across the 22 μF decoupling cap.) and VCE (voltage across the 250 μF bypass cap.) on the graph paper.

3) Remove CE from the circuit and plot the output signal.

4) Connect CE to the circuit and observe vs(t) and distortion free vL(t) on the scope again. Set the scope to ac mode. For the frequency of 1 kHz, compute ;


a) Avs = vL / vs

b) Av = vL / vi

c) Ai = iL / ii

Note: In order to obtain ii, the voltage on the 1 KΩ resistor, which is connected after signal generator, is measured and divided by the resistance value, i.e. ii = v1K / 1KΩ .

d) Zi = ? Note: You can compute Zin by using equation Zin=vi / ii , where vi is the input voltage and the ii is the input current of your circuit.

e) Zo= ? Note: In order to compute Zout; disconnect the load resistance, RL, and measure the output voltage, this is open circuit voltage, voc . Then connect a potentiometer to the output and adjust it until you

obtain the half of your voc value. At this point, measure the resistance value of the potentiometer and this is your output impedance, Zout. Comment on this method.

5)

a) Increase the magnitude of the input signal until an output signal with distortion is obtained. Draw it and explain why there is a distortion. Note the values at which distortion started.

b) Obtain the voltage transfer characteristic (vs – vL). Mark the saturation, linearity and cut off

regions.

BC 238

680 W

RL=470 W

sV (t)

1 K

Cs

CE

CL

+12 V

10 µF

47 K

470 K

33 K

2,2 K

22 µF

250 µF

+-

VL

Vi

Figure 2


1. Why do we apply a dc voltage to a transistor?

2. What is the function of CS, CL, CE capacitors?

3. Describe the linear range of transistor.


Oscilloscope BC238 (or BC548) npn transistor Signal Generator 470 KΩ pot Power Supply 47 KΩ, 33 KΩ, 2.2 KΩ, 1 KΩ, 680 Ω, 470 Ω rezistors 250 μF, 22 μF, 10 μF capacitors


Gazi University



EXP# 8 - THE CHARACTERISTICS OF JFET and JFET

AS A VOLTAGE-CONTROLLED RESISTOR

PURPOSE: This experiments aims to obtain the output (ID-VDS ) and the transfer (ID -VGS) characteristics of the JFETs as a voltage variable resistor(VVR).

PRELIMINARY WORK:

1) Consider ID-VDS curve and suggest two methods to measure the pinch -off voltage, Vp, in the laboratory.

2) If VDS is small in the order of milivolts, ID-VDS characteristics of JFET exhibit a linear and bi-directional relationship. Hence, its possible to use JFET as a resistance whose value is controlled by VGS. The JFET can be modeled as a VVR around the origin as shown in Figure 1. Show that the value of R is:

R = Vp2 / {2IDSS ( VGS - Vp )} for 0 < VDS < VGS - VP, and VP < VGS < 0.

G

D

S

G

D

S

mg

1R =

Figure1: JFET as a voltage - controlled resistance.

3. Consider the circuit of Fig. 2 :

a) Redraw the circuit of Fig.2 replacing the JFET with the model shown in Fig.1.

b) In the RC circuit, define the corner frequency and explain how you can measure it experimentally.

c) Assume VP = -3V, IDSS = 8 mA for n-channel JFET, and determine the corner frequency for VGS = 0.

d) Repeat part (c) for VGS = -2V.

R1

R2

S.G.

C= 0,1 µFV

o

-

+

V

Figure 2


1) For the Output Characteristic of JFET;

a) Set up the circuit of Figure 3 and adjust VGS = 0 volt (Be careful with polarities of DC power supply and diode).

b) Increase the VDS signal level up to 10 V ( VDSmax = 10V) at VGS = 0.

c) Draw in scale the output characteristics for 3 different values of VGS using 470 KΩ pot (for Vp < VGS < 0 volt (0, -1, -2 V)).

d) Obtain IDSS value on these curves. ( CH2 is at invert mode ).

e) In Figure 3, replace the diode with short circuit. Decrease the VDS signal level to milivolts range and observe the linear part on the oscilloscope. Determine your origin and, plot ID-VDS graph for 3 different values of VGS ( 0, -1, -2 V ).


18 K

100

BF 245CS.G.-

+

500 K 12 V

1N4001

V W

X

G D

S

Figure 3 : Circuit to display the output characteristics of an n-channel JFET.

2. For the ID - VGS Characteristic;

a) Set up the circuit of Figure 4.

b) Increase the magnitude of signal generator up to VP ( VGSmax = VP ).

c) Sketch in scale the observed waveform and obtain VP and IDSS from this curve.

1 K

270

BF 245C

S.G.

12 V

X

18 K

+

-Y

W

Figure 4

3) JFET as a voltage-controlled resistor; Set up the voltage controlled attenuation circuit of Figure 5.

a) For vin = 100 mVpp, plot the input waveform.

b) Plot the output for VGS = 0 and VGS = -1.5 Volt.

10 K

BF 245CV

in

-

+

10 K 12 V

V

1 K Vo

Figure 5


Oscilloscope 1N4001 diode Signal Generator BF245A (or BF24C) JFET Power Supply 470 KΩ pot, 10 KΩ pot AVO meter 10 KΩ, 18 KΩ, 1 KΩ, 270 Ω, 100 Ω resistors


Gazi University



EXP# 9 - JFET DC and AC ANALYSIS

PURPOSE: This experiment studies the concepts of the small-signal operation, distortion and bandwidth in common-source JFET amplifiers. The small signal parameters of the JFET will be obtained experimentally.


1. Set up the amplifier circuit in Figure 1.

100

680

+12 V

10 µF

10 µFBF 245C

10 K

Vo

(Vin)

S.G.

1 kHz W

1 K

-12 V

W

D

S

Figure 1

a) Measure ID , VDS and VGS ( disconnect the signal generator).

b) For following input values , measure dc and ac values of VDS . Find gm (how?). vin = 0.1, 0.5, 1, 1.5, 2.5 Vpp

c) Find the maximum output voltage without any distortion and record it. (Think: what causes distortion or what limits the linear operation?)

2. Set up the circuit in Figure 2. Choose Rd =1 KΩ, Rs=680 Ω.

10 K

1 K

RS

CS =250 µF

12 V

10 µF

10 µFBF 245C

10 K

Rd

Vo1

Vin

D

S

680 W

Vo2

Figure 2


a) Measure the following at the Q operating point: VDSQ, VGS

Q, ID

Q.

b) Plot Vo1 and Vo2 ( in DC mode, with and without Cs ). ( Note : Make sure that there is no distortion on the output voltages, do not forget to record the input voltage)

c) In X-Y mode, plot the transfer characteristics of the circuit. Changing the input voltage values, obtain cut-off, saturation and linear regions ( for vo1 only and with Cs). (Think: what are the definitions of those regions?)


Oscilloscope BF245C JFET Signal Generator 10 KΩ (2 pieces) Power Supply 1 KΩ AVO meter 680 Ω 100 Ω 10 μF (2 pieces) 220 μF

Question 1: For the circuit shown in Figure 3, Vp = -2V, IDSS = 1.65 mA, ID = 0.8 mA, VDD = 24V.

Assume rd >> Rd (rd is the channel resistance of the JFET), compute a) VGS, b) gm, c) Rs and d) compute the value of Rd for a minimum 20 dB voltage gain assuming Rs was by-passed with a capacitor of large value. Using the values found, plot dc and ac load lines of the circuit.

10 K

C1

RS

CS =250 µF

VDD

10 µF

10 µFBF 245C

10 K

Rd

Vo

Vin

RG

C2

D

S

Figure 3

Question 2:

a) Using the experimental results of step 1, compute IDSS and Vp of the transistor that you used (since you already know gm, ID

Q and VGS

Q, you can write equations to solve for IDSS and Vp).

b) Knowing IDSS and Vp of the transistor, calculate VGSQ and ID

Q for the circuit given in Fig. 2 and compare

them with the experimental results (of step 2-a).

c) What is the effect of Cs on the circuit in Fig. 2? Derive expressions for the voltage gain (vo1/vin) with and without Cs. Compare the theoretical results from these expressions with the experimental ones (of step 2-b). (Use gm that you found in step 1-b in the theoretical expressions.)

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