bjt lab

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High Frequency Behavior

of BJTsUniversity of Minnesota - EE 3101

[Type the author name]

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Abstract

The experiments goal is to learn how to measure the components of the hybrid- small-signal model of

the BJT and to investigate the high frequency response of some amplifier circuits using it. In this

experiment the values of the models components will be determined experimentally and then by

manipulating the amplifier circuit we can derive a series of equations to find the values of the small

signal components. The values were found to be reasonable when compared to the manufacturers data

sheets.

Introduction

The hybrid- model of a BJT is a small signal model, named after the -like equivalent circuit for a

bipolarjunction transistor. The model is shown in Figure 1. It consists of an input impedance, r , an

outputimpedance r0, and a voltage controlled current source described by the transconductance, gm.

The transconductance, gm, of a bipolar transistor is defined as the change in the collector current

divided bychange of the base-emitter voltage.

The base input resistance, r is defined by

The output resistance, ro, is defined as

However, In this experiment the model that is being used was slightly different because is being

ignored which normally is placed in parallel with will also be ignored, as the resistance will be

shunted by a much smaller resistance. The hybrid- model that will be used in this experiment is shown

below in Figure 2.With the aid of an amplifier circuit measurements will be taken to determine the

values of

Figure 1

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The digital multimeters are used in this experiment are PIX which measure voltage in rms

values.

Hybrid- Model

Using the amplifier ciruict shown in Figure 3 the input resistance of the transistor at low frequency was

measured to be 16.6k.

Using the component values shown the collector current is 0.994mA. However, the circuit that was used

in the experiement was slightly different.

was assumed to be 200 and since >>1 it can be proven that IC is equal to IE because is equal to 1.

Then using Kirchoffs voltage loop the following equation is obtained.

Vo is used as 7.5V in order to get a greater swing as requested in the experiment.

R1

100

R2

1M

R3

1k

R4

14.3k

C1

10u

C2

10u

0

V1

-15

Q2

Q2N3393

V20.1Vac

0Vdc

Figure 2

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Although RL was calculated to be 7.5K, using PSpice this did not result in a 1mA collector current where

as RL equal to 100 did, which is a considerately noticeable difference.

The base current was then calculated to be roughly 5µA using the equation; .

Using Kirchoffs voltage loop again and assuming RB to be very large, 1M, the emitter resistance was

then calculated to be 9.3K which is a lot closer to the desired value shown in Figure 1. After using these

resistor values and taking a DC analysis of the circuit trying to reach a 1mA collector current the two

resistor values were changed to 5.5K and 5.1K accordingly. However, when simulated in PSpice this

gave a 0.134mA current at the collector.

With the DC analysis Vo was measured to be 9.1V, IRE to be 1.03mA and IRL to be 1.03mA.

Then using the following formula RIN was calcualted to be 16.6K.

V1 and V2 were obtained by using the DMM to measure the voltages as shown in Figure 3 below.

RIN was higher than expected but it did coincide with what others in the same lab section

had obtained also. This discrepancy can most likely be due to the difference in component

values compared to the PSpice model above, particularly the value of RL.

Rs

Rin

+

-

OUT

V1 V2

Figure 3

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Frequency Response Part I

In the next three sections the task is to find the frequency of the BJTs single pole. To do this we will be

measuring the frequency response and finding the -3dB frequency. The current gain of the BJT behaves

according to the following equation;

Where f H is the frequency at which the current gain has fallen 3dB from its mid-band value.

Referring to the above equation it can be seen that there are a number of different variables. FH can be

found using the measurement of the -3dB point, gm can be calculated from the bias conditions and RL is

known. This leaves one equation with three unknowns. Therefore we must find another two equations

similar to this one with the same variables without introducing anymore. Later in the experiment, this

circuit is modified slightly to achieve this goal.

For now, the small signal collector current is needed. This can be measured by taking the difference in

voltage across RS which will allow us to calculate IIN. To calculate Io, the voltage across RL must be

measured then using Ohms law divided by the resistance.

The circuit that is being used for this experiment is shown in Figure 4.

Figure 4

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Gm is calculated to be 0.0385A/V using the equation;

Then using bode plotter the -3dB frequency was obtained by observing the graph output as shown

below in Figure 4.

Figure 5

FH1 was found to be 1.3MHz, gm to be 0.0385A/V and RL to be 100. With these values our first equation

becomes;

Using PSpice to simulate the same circuit the output is similar to Figure 5 but still a little different as

shown in Figure 6.

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Because the collector current measured in PSpice was not 1mA using the chosen component values the

circuit was simulated again with a 1mA current and the output was again slighly different as shown in

figure 7 below.

Each output gives a different -3dB frequency but I decided to use the frequency obtained in the lab itself

using the breadboard.

Figure 6

Figure 7

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Adding a 1nF Capacitor

In order to get the next equation a 1nF capacitor was added across the existing Cµ which lies across VBC

junction. The revised circuit is shown below in Figure 8. The values of IC and VBE have not changed;

therefore gm remains the same also.

FH2 is now measured to be 13KHz and with CX equal to 1nF, RL still equal to 100 and gm unchanged the

second equation becomes;

FH again was found using bode plotter and by observing the data graphically the -3dB point was

determined and f H was calculated. Figure 9 below shows the bode plot that was from the experiment

where as Figure 10 shows the bode plot simulated from PSpice and then Figure 11 is the bode plot of

the circuit with the 1mA collector current obtained in PSpice.

Figure 8

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Figure 11

Again simulating the circuit with the correct collector current gave a slightly different output as shown

below in Figure 11.

Figure 9

Figure 10

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Figure 12

Increase RL

In this next part the final equation is found. This time we remove the capacitor that was just previously

added and instead increased the value of RL by a factor of 10 which corresponds to a value of 1K.

f H3 is found to be 0.6MHz which gives the third equation;

The circuit that was used to find this measurement Is shown below in Figure 12.

Again, the the frequency was obtained by observing the output and taking the -3dB. Below

are three bode plots, Figure 13, 14 and 15 respectively. Figure 13 is from the labexperiment using the breadboard. Figure 14 is using PSpice with the same components as

in lab and Figure 15 is using components that make a 1mA collector current in PSpice.

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Figure 13

Figure 14

Figure 15

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Calculation of Cµ, C and r

In summary, the three equations that were previously found are;

1.

2.

3.

Solving these equations simultaneously gives the results as follows.

r= 2.5K, C=0.41pF, Cµ=1.65pF

These three values do not seem to be very reasonably for the transistors that were used in the

experiment. Obviously noisy equipment can complicates the accurate measurements needed but even

so these are noticeably wrong.

The value of rX is also required, so by using the following circuit in Figure 16 it is possible to calculate rX.

The ir it bove shows the inp t si e of the sm ll sign l hybri mo el e is nown s it is is r ete r esistor n r w s l l ted pr evio sly. in w s lso pr evio sly l l ted so rx is simple to find j stsing the series ombin tion of r esistors.

Rx

Rp

Re

0

Rin

Figure 16

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Cascode Amplifier

The circuits used up until now have been Common-Emitter amplifiers. In order to create an amplifier

with a larger bandwidth and higher gain we use a pair of transistors. This is known as a cascade amplifier

and is shown in Figure 17 below.

Figure 17

The design calls for a Vcc of 15V with a collector current of 1mA. In order to get the largest possible

output voltage swing Q1 needs to be biased around 7.5V. The three resistor values were chosen to be

200k and 100k. Then using Kirchhoffs voltage law Re was calculated to be 4.3K and RC to be 8K.

Then using Ohms law the collector current was calculated to be 0.99mA which resulted in a gain of

7.2dB which gave a f L=230Hz and f H=208KHz resulting in a bandwidth of 208KHz.

However, when simulated in PSpice using these calculated values the collector current was then

observed to be roughly 0.5mA so Re was adjusted accordingly until 1mA was obtained. Re reached 1.9K

before the desired current was reached.

Figure 18 below shows the bode plot from PSpice using the circuit from Figure 17. The bandwidth in that

circuit was a lot larger and approximately 5MHz.

0

R

¡

7.9k

R ¢

£ 00k

R

¤

00k

R

6

00k

R

7

.9k

C8

0u

C9

47¥

C

0

47¥

¦ ¤

¦ £

N¡ ¡

93

Q6

Q2N3393

V7

§

¤

V

V80.1Vac

0V ̈

c

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Figure 18

Common-Collector/Common-Base Transistor Pair

This amplifier should be able to operate with a larger bandwidth but everything comes with a price and

this time it will cost some gain. The capacitors that are being used for coupling in this circuit are 10µF

and then a 47µF capacitor between the emitters. The goal is to achieve a 1mA collector current in Q2. To

find the gain and bandwidth a series of voltage measurements are taken at VO and VS verses frequency.

Figure 19, as shown below is the circuit that was constructed in both PSpice and on the breadboard.

Figure 19

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VO was measured to be 7.2V.

The upper corner frequency is caused by the transistors high frequency limitations. The upper corner

frequency was found to be roughly 230 KHz which is a gain of 1.65. The lower corner frequency occurs

around 100Hz which is caused by the coupling capacitors shorting out from the very low frequency. The

-3dB point is 4.4dB which is a gain of 2.36 approximately.

Because a resistance was added to the source it altered the measurements so Vi and VO measurements

were taken again and the gain increased to 16.1.

The circuit that was used to make these measurements is shown below in Figure 20.

Comparison of Amplifier Topologies

This section is simply comparing the circuits of the previous sections to the cascade circuits. There were

a total of three circuits used in the experiment; a single-transistor current follower was the first one.

This proved to have acceptable gain and bandwidth. However, when using a pair of transistors the gain

and bandwidth improved. Then using the Cascode circuit in PSpice the gain decreased where as the

bandwidth increased.

C141n

0

R18

7 9

R19

200k

R 0

100k

R

1100k

R

1 9k

C11

10u

C13

47n

7

N3393

V9

-15V

V100.1Va

0V

8

N3393

Figure 20

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Conclusion

The Hybrid- model, as complicated as it may seem is used for many various applications. With simply

altering the amplifier circuits slightly the gain and bandwidth can have a major effect from it. Working at

such frequencies in the lab made it very difficult to record accurate measurements because the

instruments were susceptible to noise, even directly from the function generator were difficult to

accurately record data using the oscilloscope. There is a good chance that this is one reason why the

data obtained during the experiment was a little different than anticipated. The fact that some of these

amplifier circuits produce large amounts of gain which require small input signals to avoid the output

being clipped. This made it very hard to observe the input when it was small.

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