Radio Frequency Integrated Circuit Design - Webs

184 Radio Frequency Integrated Circuit Design
when the bias is applied this way, the emitter is at a virtual ground. This means
that for small-signal differential inputs, this voltage never moves from its nominal
voltage.
This stage can be used in many circuits such as mixers, oscillators, or
dividers. If an input voltage is applied larger than about 5vT , then the transistors
will be fully switched and they can act as a limiting stage or ‘‘square wave
generator’’ as well.
All the equations already developed are still valid for the differential
amplifier. The large signal current and voltage relationships are often written
as hyperbolic tangents. The currents are given by
iC1 =
iC2 =
IEE 1 + e −(v1 /vT ) = IEE 2 �1 + tanh� v 1
2vT��
IEE 1 + e (v1 /vT ) = IEE 2 �1 − tanh� v 1
2vT��
and the differential output voltage is given by
vo2 − vo1 = IEERC tanh� v 1
2vT�
(6.96)
(6.97)
(6.98)
Note that there will only be even-order terms in a power series expansion
of this nonlinearity and hence no dc shifts or even harmonics in vo2 − vo1 as
v 1 grows.
The slope at v 1 = 0 will be
∂iC2
∂v 1
= ∂iC2 =−
2∂v BE2
1
2 g m2 =− 1 IC2
=−
2 vT
IEE
4vT
(6.99)
This can be found directly by taking the derivative of the above equation
for iC2 and setting v 1 to 0.
6.6 Low-Voltage Topologies for LNAs and the Use of On-
Chip Transformers
Of the configurations described so far, the common-emitter amplifier would
seem ideally suited to low-voltage operation. However, if the improved properties
of the cascode are required at lower voltage, then the topology must be modified
slightly. This has led some designers to ‘‘fold’’ the cascode as shown in Figure