Small Signal Voltage Gain next up previous
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Small Signal Voltage Gain

For the sake of understanding, it's useful to connect a passive load resistor, RL to the output of the diff-amp as shown in Fig.6.2 [6.2]. Now, let's use the the `delta' method to determine the small signal gain of this configuration.

For the sake of understanding, let's assume we take the small signal output from the collector of Q2, and input the small signal voltage to the base of Q1. The midband small signal voltage gain will then be defined as the change in the collector voltage at Q2 divided by the change in the base voltage of Q1, or $A_v=\frac{V_o}{V_i}=\frac{\Delta V_{c2}}{\Delta V_{b1}}$.To find the small signal change in the input, we start with the large signal KVL equation

Vb1-Vb2= Vbe1-Vbe2  

Now, if we ground Vb2, and make a small signal change in Vb1 we obtain

 

Recall from previous labs that a first order Taylor series gives $\Delta V_{be}=\frac{\Delta I_c}{g_m}$.We then find that

 

Since $g_m=\frac{I_C}{V_t}$ and, under DC conditions IC1=IC2, then

gm1=gm2=gm

Now, recall that the total DC bias current in the diff-amp is IEE which is fixed. Thus, if we make a small increase in Ic1 then there will be a corresponding small decrease in Ic2. We express this mathematically by taking the small signal change of equation ([*]), which gives

which leads to

Also, continuity ensures that $\Delta I_{c1}~=~\Delta I_{c3}$, and current mirror operation dictates that $\Delta I_{c3}~=\Delta I_{c4}$.Now let's look at the current to the load resistor RL. KCL says that

Where IL is the current into the load resistor RL, and $V_o=\Delta I_{L}R_L$.If we express all small signal currents in terms of $\Delta I_{c1}$,we can arrive at the following expression for Vo.

Vo=2DIc1RL

If we divide the output voltage by the input voltage given in equation ([*]), we obtain the following expression for midband gain.

Av=Vo/ Vin=gmRL

next up previous
Next: Collector Output Resistance (Early Up: Differential Amplifier with Active Previous: DC Bias
Bassel Al-Annouf
12/7/1998