Question 5.23: For the common-base amplifier of Fig. 5.121 , determine the ...
For the common-base amplifier of Fig. 5.121 , determine the following parameters using the complete hybrid equivalent model and compare the results to those obtained using the approximate model.
a. Z_i
b. A_i
c.A_{v} .
d. Z_o
The common-base hybrid parameters are derived from the common-emitter parameters using the approximate equations of Appendix B :
h_{i b} \cong \frac{h_{i e}}{1+h_{f e}}=\frac{1.6 k \Omega}{1+110}= 1 4 . 4 1 \OmegaNote how closely the magnitude compares with the value determined from
h_{i b}=r_{e}=\frac{h_{i e}}{\beta}=\frac{1.6 k \Omega}{110}=14.55 \OmegaAlso, h_{r b} \cong \frac{h_{i e} h_{o e}}{1+h_{f e}}-h_{r e}=\frac{(1.6 k \Omega)(20 \mu S )}{1+110}-2 \times 10^{-4}
=0.883 \times 10^{-4}
h_{f b} \cong \frac{-h_{f e}}{1+h_{f e}}=\frac{-110}{1+110}=- 0 . 9 9 1
h_{o b} \cong \frac{h_{o e}}{1+h_{f e}}=\frac{20 \mu S }{1+110}= 0 . 1 8 \mu S
Substituting the common-base hybrid equivalent circuit into the network of Fig. 5.121 results in the small-signal equivalent network of Fig. 5.122 . The Thévenin network for the input circuit results in R_{T h}=3 k \Omega \| 1 k \Omega=0.75 k \Omega for R_s in the equation for Z_o .
a. Eq. (5.169):
Z_{i}=\frac{V_{i}}{I_{i}}=h_{i}-\frac{h_{f} h_{r} R_{L}}{1+h_{o} R_{L}} (5.169)
Z_{i}^{\prime}=\frac{V_{i}}{I_{i}^{\prime}}=h_{i b}-\frac{h_{f b} h_{r b} R_{L}}{1+h_{o b} R_{L}}
=14.41 \Omega-\frac{(-1.991)\left(0.883 \times 10^{-4}\right)(2.2 k \Omega)}{1+(0.18 \mu S )(2.2 k \Omega)}
= 14.41 Ω + 0.19 Ω
= 14.60 Ω
versus 14.41Ω using Z_{i} \cong h_{i b}; and
Z_{i}=3 k \Omega \| Z_{i}^{\prime} \cong Z_{i}^{\prime}= 1 4 . 6 0 \Omegab. Eq. (5.167):
A_{i}^{\prime}=\frac{I_{o}}{I_{i}^{\prime}}=\frac{h_{f b}}{1+h_{o b} R_{L}}=\frac{-0.991}{1+(0.18 \mu S )(2.2 k \Omega)}
= -0.991
Because 3 k \Omega \gg Z_{i}^{\prime}, I_{i} \cong I_{i}^{\prime} and A_{i}=I_{o} / I_{i} \cong- 1.
c. Eq. (5.168):
A_{v}=\frac{V_{o}}{V_{i}}=\frac{-h_{f} R_{L}}{h_{i}+\left(h_{i} h_{o}-h_{f} h_{r}\right) R_{L}}=\frac{-(-0.991)(2.2 k \Omega)}{14.41 \Omega+\left[(14.41 \Omega)(0.18 \mu S )-(-0.991)\left(0.883 \times 10^{-4}\right)\right] 2.2 k \Omega}
= 149.25
versus 151.3 using A_{v} \cong-h_{f b} R_{L} / h_{i b}.
d. Eq. (5.170):
Z_{o}=\frac{V_{o}}{I_{o}}=\frac{1}{h_{o}-\left[h_{f} h_{r} /\left(h_{i}+R_{s}\right)\right]} (5.170)
Z_{o}^{\prime}=\frac{1}{h_{o b}-\left[h_{f b} h_{r b} /\left(h_{i b}+R_{s}\right)\right]}
=\frac{1}{0.18 \mu S -\left[(-0.991)\left(0.883 \times 10^{-4}\right) /(14.41 \Omega+0.75 k \Omega)\right]}
=\frac{1}{0.295 \mu S }
= 3.39 M Ω
versus 5.56 M Ω using Z_{o}^{\prime} \cong 1 / h_{o b}. For Z_o as defined by Fig. 5.122 ,
Z_{o}=R_{C}\left\|Z_{o}^{\prime}=2.2 k \Omega\right\| 3.39 M \Omega= 2 . 1 9 9 k \Omegaversus 2.2 kΩ using Z_{o} \cong R_{C}
