Tune In

The problem

Build a common-source amplifier whose load is a tank: an inductor from VDD to “out”, a capacitor from “out” to ground, and a resistor from VDD to “out” that stands for the inductor’s losses and sets the Q. The test bench adds 100 fF of load. Choose L, C and the resistor so that the gain peaks between 1.8 GHz and 2.3 GHz, with a peak gain of at least 5 dB and a −3 dB width of the peak between 60 MHz and 400 MHz.

An inductor and a capacitor in parallel resonate at f₀ = 1/(2π√(L·C)): at that frequency their impedances cancel and the load looks like the loss resistor in parallel with the transistor’s own output resistance. Below it the inductor shorts the output to VDD, above it the capacitor shorts it to ground. The result is a narrow gain peak, used in radios to select one channel and reject the others.

The test bench

• Supply: VDD = 1.8 V.
• The test bench hangs a 100 fF load capacitor from “out” to ground and applies the AC stimulus to “in”. It sweeps from 100 MHz to 10 GHz (100 points per decade) and finds the frequency and level of the highest gain.

Numbers to hit

• ◆Frequency of the gain peak between 1.8 GHz and 2.3 GHz
• ◆Peak gain at least 5 dB
• ◆−3 dB width of the peak between 60 MHz and 400 MHz
• ◆Output DC level between 1.5 V and 2 V