Radio Frequency Integrated Circuit Design - Webs

High-Frequency Filter Circuits
inside the transistor model starts to dominate, then these transistors will need
to be made bigger. The inductor L was chosen so that L = 1 nH and the Q
was assumed to be 10. This generated a parallel resistance across the resonator
of 440� at 7 GHz. This meant that the capacitors were initially sized so that
C = 1.03 pF for a center frequency of 7 GHz. In simulation, they were adjusted
to be 825 fF to account for parasitic capacitance. Since the resonator had a
loss from the inductor of 440� this meant that 2/g m = 440�. Thus, IC = 114
�A and therefore I sharp = 227 �A. Note that this simple analysis does not take
into account transistor losses such as base resistance or output resistance. Through
simulation, this current was refined to 337 �A. A plot of the gain with this
current in the resonator is shown in Figure 9.18. This shows a very deep notch
that reaches a depth of about −55 dB.
Of course, even with feedback, this current will never be able to be set
with absolute precision. If the current varies by 5% either to 328.6 or 345.4
�A, then the notch depth drops to 28 dB, as shown in Figure 9.19. The noise
figure of this design was also simulated and was found to rise to 2.7 dB. Table
9.1 also shows these numbers for direct comparison of the two designs.
Finally, the design was simulated with increasing input voltage to find
out how large the signal could be made before the image rejection started to
degrade. The current Isharp was set to 345 �A and the voltage at the notch
frequency was raised slowly in a transient simulation. As shown in Figure 9.20,
image rejection in this design starts to degrade at about 1 mV. This is still a
very small signal. Thus, work still needs to be done to increase the signal
handling of this design. One thing that would help would be if the resonator
Figure 9.18 Simulated S 21 for the LNA with notch filter.
345