Radio Frequency Integrated Circuit Design - Webs

200 Radio Frequency Integrated Circuit Design
io = (Io + g mcv1) tanh v 2
2vT
= Io tanh v 2
2vT
�
+ g mcv1 tanh v 2
2vT
�
v 2 feedthrough multiplication (mixing)
(7.4)
We note that feedthrough appear equally in the output voltages above
(common mode), and so does not appear in the differential output voltage.
7.5 Double-Balanced Mixer
In order to eliminate the v 2 feed-through, it is possible to combine the output
of this circuit with another circuit driven by −v 2, as shown in Figure 7.3. This
circuit has four switching transistors known as the switching quad. The output
current from the second differential pair is given by
io ′ = i 6 − i 5 = Io tanh v 2
2vT − g mcv1 tanh v 2
2vT
Therefore the total differential current is
iob = io − io ′ = 2g mcv1 tanh v 2
2vT
(7.5)
(7.6)
This removes the v 2 feed-through term that was present in (7.4).
The last step in making this circuit practical is to replace the ideal current
sources with an actual amplifier stage, as shown in Figure 7.4. Now v 1 is applied
Figure 7.3 Double-balanced transconductance-controlled mixer.