Question 11.2: Calculating Performance of Cascaded Amplifiers Consider the ...

Considering loading by the input resistance of the second stage, the voltage gain of the first stage is

A_{v1}=\frac{v_{o1}}{v_{i1}}=\frac{v_{i2}}{v_{i1}}=A_{voc1}\frac{R_{i2}}{R_{i2}+R_{o1}}=150

where we have used the fact that A_voc1 = 200, as indicated in Figure 11.6. Similarly,

A_{v2}=\frac{v_{o2}}{v_{i2}}=A_{voc2}\frac{R_{L}}{R_{L}+R_{o2}}=50

The overall voltage gain is

A_v=A_{v1}A_{v2}=7500

Because R_i2 is the load resistance for the first stage, we can find the current gain of the first stage by use of Equation 11.3:

A_i=\frac{i_o}{i_i}=\frac{v_o/R_L}{v_iR_i}=A_v\frac{R_i}{R_L}           (11.3)

A_{i1}=A_{v1}\frac{R_{i1}}{R_{i2}}=10^5

Similarly, the current gain of the second stage is found as

A_{i2}=A_{v2}\frac{R_{i2}}{R_{L}}=750

The overall current gain is

A_i=A_{i1}A_{i2}=75\times 10^6

Now, the power gains can be found as

G_1=A_{v1}A_{i1}=1.5\times 10^7

G_2=A_{v2}A_{i2}=3.75\times 10^4

and

G=G_1G_2=5.625\times 10^{11}