Radio Frequency Integrated Circuit Design - Webs

202 Radio Frequency Integrated Circuit Design
Then, assuming that the amplifier formed by Q 1 and Q 2 is linear,
(i 3 + i 5) − (i 4 + i 6) = tanh� v 2
2vT� (i 1 − i 2) = tanh� v 2 v 1
2vT� re + R E
(7.10)
The output differential voltage is
vo =−tanh� v 2 v 1
R C
2vT� re + R E
Thus, the gain of the circuit relative to v 1 can be determined:
vo v 1 =−tanh� v 2 R C
2vT� re + R E
(7.11)
(7.12)
With R E = 0, a general large-signal expression for the output can also be
written:
vo =−2R C Io tanh� v 1
2vT� tanh� v 2
2vT�
(7.13)
This takes into account nonlinearity from the bottom pair as well as from
the top quad. Previously, with R E present, the bottom was treated in a linear
fashion.
7.6 Mixer with Switching of Upper Quad
Usually, a downconverting mixer is operated with v 1 as the RF signal and v 2
as the local oscillator. The RF input must be linear, and linearity is improved
by the degeneration resistors. Why must the RF input be linear? In a communications
receiver application, the RF input can have several channels at different
frequencies and different amplitudes. If the RF input circuitry were nonlinear,
adjacent channels could intermodulate and interfere with the desired channel.
For example, with inputs at 900, 900.2, and 900.4 MHz, if 900 MHz is desired,
the third-order intermodulation term from the two other signals occurs at
2 � 900.2 − 900.4 = 900 MHz, which is directly on top of the desired signal.
The LO input need not be linear, since the LO is clean and of known
amplitude. In fact, the LO input is usually designed to switch the upper quad