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AE_Lecture 5_Part C_continued_high frequency analysis of CE & CC

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: This is the continuation of AE_Lecture 5 _ Part C. We saw in the last part how the B.W. is determined for CB Amplifier. In this continuation of Part C , we do the high frequency analysis of CE and CC amplifier by Open Circuit Time Constant Method.This part is concluded by a Table where we give the Comparative Study of Performance Parameters of CE,CB and CC Amplifier. There will be a final concluding part of Lecture 5_PartC where we will show the simulation results of CE,CB and CC amplifier in frequency domain.

AE_Lecture 5_Part C_continued_high frequency analysis

of CE & CC

Figure 1
Figure 1 (Picture 4.png)

In Figure 1 we have RC-coupled CE BJT Amplifier. This has a Q point (ICQ = 1mA, VCEQ = 5V). The Hybrid- π parameters are same as in last chapter namely:

β fo = incremental short circuit gain at low frequencies = 100;

Transit frequency given = f T = 200MHz;

At the Q point, C ob = C µ = C jBC =

Figure 2
Figure 2 (graphics1.png)
= 5pF ;

Circular Transit Frequency = ω T =

Figure 3
Figure 3 (graphics2.png)
1.2566×10 9 radians/second;

Trans-conductance = g m =

Figure 4
Figure 4 (graphics3.png)
40mSiemens(or mS) =
Figure 5
Figure 5 (graphics4.png)
= 1/25Ω;

Whereas

Figure 6
Figure 6 (graphics5.png)
;

Figure 7
Figure 7 (graphics6.png)

Base spreading resistance is given as r x =100Ω ;

Figure 8
Figure 8 (graphics7.png)

The circuit elements are given as :

RC = 5k, RE = 2k, R1 = 200k, R2 = 60k, RL = 100k , RS = 50Ω,

RB = R1 || R2=46k, RL′ = 5k||100k = 4.76k;

Under incremental condition, the circuit is represented as Figure 2. Bias Supply VCC is shorted, coupling capacitances CC1 and CC2 are shorted and Emitter Bypass Capacitance CE is is shorted.

Figure 9
Figure 9 (Picture 5.png)

For incremental analysis at high frequencies, BJT is replaced by its corresponding high frequency Hybrid-π Model as shown in Figure 3.

Figure 10
Figure 10 (Picture 6.png)

In the beginning of the Lecture 5 we have already discussed that the number of energy storage elements decide the order of the system and accordingly the number of poles. We have also discussed that in Low Pass Filter situation if the lowest pole is well below the higher poles then it is the dominant pole and it decides the higher -3dB frequency (fh) and in High Pass Filter situation the highest pole decides the lower -3dB frequency (fl).

In the present case by inspecting the incremental circuit diagram, we find two Capacitances , Cπ and Cμ . Each has its open circuit time constant , τ10 and τ20 respectively.

Effective time constant τeff = τ10 + τ20 ;

Therefore ωh =

Figure 11
Figure 11 (graphics8.png)
= higher -3dB frequency (2πfh);

Fortunately by applying Miller Transformation we can make single pole approximation of the incremental circuit.

By Miller Transformation, Cμ is transformed as:

Figure 12
Figure 12 (graphics9.png)
at the input pair of nodes b׳ e and

Figure 13
Figure 13 (graphics10.png)
at the output pair of nodes ce.

Here AV0 = -gmRC||RL = midband gain of the basic CE amplifier.

Figure 14
Figure 14 (graphics11.png)
is known as Miller Multiplicaion Factor and

Figure 15
Figure 15 (graphics12.png)
is known as the Miller Capacitance.

Therefore total Capacitance appearing at the input node pair is:

CT = Cπ +

Figure 16
Figure 16 (graphics13.png)
= 29pF +5pF(1+180)= 934pF;

Hence the incremental circuit is modified to the circuit shown in

Figure 4 with single pole approximation :

Figure 17
Figure 17 (Picture 7.png)

The equivalent resistance seen by CT by inspection is:

Figure 18
Figure 18 (graphics14.png)
;

Therefore ωh =

Figure 19
Figure 19 (graphics15.png)
;

Thererfore fh = 1/0.8304μsec = 1.2MHz;

The mid-frequency analysis gives the Midband Voltage Gain as :

Figure 20
Figure 20 (graphics16.png)
= -177.36;

AVO = -183.076

High Frequency Analysis of CC Amplifier.

In Figure 5, the circuit configuration of CC Amplifier or more commonly known as Emitter Follower is given. This has a Voltage Gain of Unity hence it is always used as a Buffer with a very large input impedance and a very low output impedance. Hence emitter follower is ideal for driving variable loads and transmission lines. This also helps isolate the load from the Amplifier Circuit thereby ensuring maximum voltage gain of the Amplifier Circuit. If the load is not isolated then loading will occur and Voltage Gain will fall.

Figure 21
Figure 21 (Picture 8.png)

The incremental representation of CC BJT Amplifier is given

in Figure 6. In the incremental representation, biasing Battery is treated as short. CC1 , CC2 and CC are also treated as a short circuit.

Figure 22
Figure 22 (Picture 9.png)

Replacing BJT by Hybrid-π model we get the incremental representation as shown in Figure 7.

Figure 23
Figure 23 (Picture 10.png)

By inspection we see that we have capacitances ; Cπ and Cμ . They have their associated open circuit time constants τ10 and τ20 . For determining these time constants we must know the open circuit resistances seen by Cπ and Cμ .

The equivalent resistance R10 is seen by Cπ can be determined from Figure 8.

Figure 24
Figure 24 (Picture 11.png)

Total current drawn from the voltage source vo is io = ix + iπ ;

Where iπ =

Figure 25
Figure 25 (graphics17.png)
;

And in the second path of base spreading resistance (rx) :

We have vo= ix (rx + RS||RB + RE||RL) – βfoiπ RE

= ix (rx + RS||RB + RE||RL) – βfo×RE×

Figure 26
Figure 26 (graphics18.png)

= ix (rx + RS||RB + RE||RL) – gm×RE×

Figure 27
Figure 27 (graphics19.png)

Rearranging the terms we get: vo/ix =

Figure 28
Figure 28 (graphics20.png)

Therefore R10

Figure 29
Figure 29 (graphics21.png)

Substituting the parameter and element values we get :

R10

Figure 30
Figure 30 (graphics22.png)

The equivalent resistance seen by Cμ is R20 . This equivalent resistance can be determined by the Figure 9.

Figure 31
Figure 31 (Picture 12.png)

By inspection we see that there are two currents flowing out of the source v0 . The two currents are ix and iπ .

The current ix sees the resistance (rx + RS||RB).

The current iπ sees the resistance [rπ + (1+βfo) RE||RL].

Therefore R20 = (rx + RS||RB)|| [rπ + (1+βfo) RE||RL]

Substituting the parameter values and element values in the above equation we get:

R20 = (100 + 50)|| [2500 + (1+100) 2000] = 150Ω

Therefore τ10 = R10×Cπ = 26.54Ω×29pF = 769.66psec.

And τ20 = R20×Cμ = 150Ω×5pF = 750psec.

Therefore fh =

Figure 32
Figure 32 (graphics23.png)

Referring to Figure 6, we can determine the midband overall gain:

Figure 33
Figure 33 (graphics24.png)
≈ 1

Here we have assumed that loading by RB has been removed by boot-strapping technique. As can be seen from the formula above, the internal gain and overall gain including RS is the same.

Determination of the output impedance of CC Amplifier:

Determination of the output impedance of CE and CB is quite straight forward.

Rout =

Figure 34
Figure 34 (graphics25.png)
in CE Amplifier. The default value of
Figure 35
Figure 35 (graphics26.png)
= 40k.

Rout =

Figure 36
Figure 36 (graphics27.png)
in CB Amplifier. The default value of
Figure 37
Figure 37 (graphics28.png)
= 2M.

For CC amplifier we will have to go to the incremental model with source inactivated and a source vo applied at the output pair of nodes as shown in Figure 10:

Figure 38
Figure 38 (Picture 13.png)

By inspection we see that output current from the applied source is flowing through three paths:

Through RE we have ie flowing.

Through (rπ + rx + RS||RB) we have ib (controlling current) flowing.

Through controlled source we have βfoib flowing.

Hence total current io = ie + ib + βfoib

= vo(

Figure 39
Figure 39 (graphics29.png)
vo(
Figure 40
Figure 40 (graphics30.png)

Therefore Rout as seen by vo is

Figure 41
Figure 41 (graphics31.png)
≈
Figure 42
Figure 42 (graphics32.png)
= 25Ω.

Hence output impedance of CC Amplifier is 25Ω but input impedance is 200kΩ. Therefore CC Amplifier acts as voltage controlled voltage source with unity voltage gain hence it is ideal for BUFFER applications as well as for driving transmission lines and for driving variable loads.

In Table 1, we make a comparative study of the performance parameters of the three configurations of BJT Amplifier.

Table 1. Comparative study of the performance parameters of CE,CB and CC amplifier.

Table 1
  AVSO(Overall gain) AVO(Internal gain) Band width Rin Rout
CE -177.36 -183.07 1.2MHz 2.6k 40k= 1/hoe
CB 63.4 190.4 6.5MHz 25Ω 2M = 1/hob
CC 0.987 0.987 104.73MHz 204.6k 25Ω

As can be seen from the Table 1, the internal gain and overall gain are different only in CB. In the remaining two configurations the gains are approximately the same.

Also Open Circuit Time Constant method gives a conservative value of upper -3dB frequency and Short Circuit Time Constant method also gives a conservative value of lower -3dB frequency. The actual BW is 1.1 times larger than the calculated values.

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