Radio Frequency Integrated Circuit Design - Webs

182 Radio Frequency Integrated Circuit Design
Also, it should be noted that this relationship only holds true if the transistor
does not start to saturate. If it does, the nonlinearity will get much worse.
6.4.3 High-Frequency Nonlinearity in the Bipolar Transistor
Many frequency-dependent devices can reduce the linearity of a circuit. One
of the most troublesome is the base-collector junction capacitance C� . This
capacitance is voltage dependent, which results in a nonlinearity. This nonlinearity
is especially important in circuits with low supply voltages because the
capacitance is largest at low reverse bias.
This capacitor’s effect is particularly harmful for both frequency response
and nonlinearity in the case of a standard common-emitter amplifier. In this
configuration, C� is multiplied by the gain of the amplifier (the Miller effect)
and appears across the source.
The value of C� as a function of bias voltage is given by
C� (V ) =
C�o
�1 − V
� o� (1/n)
(6.94)
where C�o is the capacitance of the junction under zero bias, � o is the builtin
potential of the junction, and n is usually between 2 and 5. Since this
capacitor’s behavior is highly process dependent and hard to model, there is
little benefit in deriving detailed equations for it. Rather, the designer must rely
on simulation and detailed models to predict its behavior accurately.
6.4.4 Linearity in Common-Collector Configuration
The common-collector amplifier is often called the emitter-follower because the
emitter voltage ‘‘follows’’ the base voltage. However, the amplifier cannot do
this over all conditions. If the current is constant, vBE is constant and the
transfer function will be perfectly linear. However, as vo changes, and iout =
vo /R out will change as shown in Figure 6.31. Thus, iE will change and so will
vBE, and there will be some nonlinearity.
If R out is large so that iout is always much less than IB , the linearity will
be good, as the operating point will not change significantly over a cycle of the
signal. It is important to keep the peak output current less than the bias current.
This means that
|v o,peak|
R out < IB (6.95)