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AE_Lecture 5_Part C_continued_High frequency analysis of CB.

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_Lecture 5_Part C_CB gives the high frequency analysis of CB Amplifier while using a common self biasing network. We can use the same self-biasing network to realize CB,CE and CC and then make a comparative study of their upper cu-off frequency.

AE_Lecture 5_Part C_continued_High frequency analysis of CB.

In this continuation of high frequency application, we use the same self-biasing configuration to achieve CB, CE and CC amplifier. These three Circuit Configuration have the same Q point ( ICQ = 1mA , VCEQ = 5V). Hence they have the same Hybrid-π parameters in all three configurations 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 1
Figure 1 (graphics1.png)
= 5pF ;

Circular Transit Frequency = ω T =

Figure 2
Figure 2 (graphics2.png)
1.2566×10 9 radians/second;

Here it may be noted that reciprocal of frequency gives Time Period of repetition T but reciprocal of circular frequency always gives the Time –Constant. In filters the reciprocal of circular cut-off frequencies gives the RC time constant of the associated RC configuration. Here the reciprocal of the circular transit frequency gives the transit time across the narrow base of the BJT .

Transit Time =

Figure 3
Figure 3 (graphics3.png)
0.8nsec;

Trans-conductance = g m =

Figure 4
Figure 4 (graphics4.png)
40mSiemens(or mS) =
Figure 5
Figure 5 (graphics5.png)
= 1/25Ω;

Whereas

Figure 6
Figure 6 (graphics6.png)
;

Figure 7
Figure 7 (graphics7.png)

Therefore

Figure 8
Figure 8 (graphics8.png)

Therefore

Figure 9
Figure 9 (graphics9.png)

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

Figure 10
Figure 10 (graphics10.png)
Figure 11
Figure 11 (Picture 1.png)

Self –biasing configuration is connected as CE BJT Amplifier by the use of Emitter bypass capacitance CE.

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;

The same configuration can be connected as CB Amplifier by the use of Base bypass capacitance CB as shown in the Figure 3. The same configuration can be connected as CC Amplifier by the use of Collector bypass capacitance CC as shown in the Figure 4.

Figure 12
Figure 12 (Picture 2.png)

High Frequency Analysis of CB Amplifier:

Under incremental condition (refer to Figure 3),

CB shorts out R1 and R2 . Coupling capacitors appear as short circuit. Battery VCC appears as short circuit. Hence the incremental circuit of CB amplifier is the following as shown in Figure 5 :

Figure 13
Figure 13 (Picture 3.png)

For circuit analysis we replace CB configuration of BJT with its corresponding T-Model as shown in Figure 6.

Figure 14
Figure 14 (Picture 4.png)

In Figure 6, b׳ is the active base region and b is the external base terminal. The T-Model is further re-oriented as two input and output loop as shown in Figure 7.αfo

Figure 15
Figure 15 (Picture 5.png)

The T-Model of CB BJT is further simplified into two non-interacting loops as shown in Figure 8.

Figure 16
Figure 16 (Picture 6.png)

Base spreading resistance rx is reflected as (1-αfo)rx in input loop and in output loop it is not reflected since it is controlled loop. Since (1-αfo)rx is a negligible resistance hence in input loop it has been completely neglected as a result the input and output loops are completely non-interacting. This is the reason reverse transmission factor is almost non-existent in CB BJT and it is a near-Unilateral device. Hence it is very suitable for RF applications. RF Amplifier are very prone to parasitic oscillations. But if we use a Unilateral Active Device the possibility of parasitic oscillation is minimal.

Referring to Figure 8, we see there are two capacitors Ce and Cc. Both have two time-constants associated with them.

R10 as seen by Ce is re||RE||RS = 25Ω

Therefore time constant associated with Ce = τ10 = 29pF.25Ω=725psec.

R20 as seen by Cc is RC||RL = 4.76kΩ

Therefore time constant associated with Cc = τ20

=5pF.4.76kΩ=2380psec.

Figure 17
Figure 17 (graphics11.png)

Therefore higher cut-off frequency = fh = 6.489kHz.

Midband Voltage Gain w.r.t. source (shown previously)

=

Figure 18
Figure 18 (graphics12.png)
=
Figure 19
Figure 19 (graphics13.png)
= 63.4

Internal Voltage Gain =

Figure 20
Figure 20 (graphics14.png)
.

Note these are non-inverting gains.

In the lab, we will get vastly different gains by including source resistance and neglecting source resistance. So while making voltage gain measurement we have to be careful as to which gain we are measuring.

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