In addition to maximizing power transfer, impedance-transforming networks are widely used simply to enable a specific amount of power to be delivered to a load. An important example is found in the output stage of a transmitter where, owing to supply voltage limitations, a downward impedance transformation of the antenna resistance is necessary. A common load impedance is 50 ohms. Suppose we wish to deliver 1 W of power into such a load at 1 GHz, but the power amplifier has a maximum peak-to-peak sinusoidal voltage swing of only 6.33 V because of various losses and transistor breakdown problems. Design the following matching networks to allow that 1 W to be delivered. Use low-pass versions in all cases, and assume that all reactive elements are ideal (if only that were true ... )
(a) L-match.
(b) pi-match (Q = 10)
(c) T-match (Q = 10)
(d) 2 section L-match
(e) If the maximum allowable on-chip capacitance is 200 pF and the maximum allowable onchip inductance is 15 nH, are any of your designs amenable to a fully integrated implementation? If so, which one(s) ?
(f) Simulate (a) , (b) , (c) and (d) using LTspice:
Do a frequency sweep from 0 Hz to 5 GHz:
Plot the transfer function (Vo/Vi) vs. frequency. Make sure (Vo/Vi) is expressed in dB
Plot the input impedance of the matching network vs. frequency (real and imaginary in different graphs)
Compare the frequency response of (a) , (b) , (c) and (d) , which one will give you more bandwidth? Calculate the 3dB bandwidth of each topology.