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 ( I_CQ = 1mA , V_CEQ = 5V). Hence they have the same Hybrid-π parameters 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 =

= 5pF ;

Circular Transit Frequency = ω T =

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 =

0.8nsec;

Trans-conductance = g m =

40mSiemens(or mS) = = 1/25Ω;

Whereas

;

Therefore

Therefore

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

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

The circuit elements are given as :

R_C = 5k, R_E = 2k, R₁ = 200k, R₂ = 60k, R_L = 100k , R_S = 50Ω,

R_B = R₁ || R₂=46k, R_L^′ = 5k||100k – 4.76k;

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

High Frequency Analysis of CB Amplifier:

Under incremental condition (refer to Figure 3),

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

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

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.

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

Base spreading resistance r_x is reflected as (1-α_fo)r_x in input loop and in output loop it is not reflected since it is controlled loop. Since (1-α_fo)r_x 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 r_e||R_E||R_S = 25Ω

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

R₂₀ as seen by Cc is R_C||R_L = 4.76kΩ

Therefore time constant associated with Cc = τ₂₀

=5pF.4.76kΩ=2380psec.

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

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

=

= = 63.4

Internal Voltage Gain =

.

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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This work is licensed by Bijay_Kumar Sharma under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.

Last edited by Bijay_Kumar Sharma on Mar 21, 2010 9:37 pm -0500.