ECE202A, problem set 2a, due Monday Nov. 1, 1999
An Impedance-matching exercise…
The transistor we will use as a design vehicle has the model below.
Ri
Cgs
Rds
gmVgs
gm=100 mS, Cgs=0.32 pF, Rds=200 Ohms, Ri=10 Ohms
1) At a design frequency of 20 GHz, using the Smith chart (working by hand), find the
values of the network below to match the input to 50 Ohms
2) At a design frequency of 20 GHz, Using the Smith Chart, design a series/shunt stub
tuner to match the input to 50 Ohms.
3) ***using EESOF*** (and *not* analyzing by hand first), design the matching network
below. The steps are
(1) add the 100 Ohm line first and adjust its length to obtain a (normalized to 50 Ohms)
admittance of 1+jB. B needs to be positive.
(2) then add the shunt capacitor to make the total admittance zero.
1
port 2
100 Ohm line
port 1
Construct the network, as indicated, as a two-port, and plot S11 and S21 to examine the
gain and reflection coefficient as a function of frequency.
4) Broadband matching networks: Often we desire to have a wideband amplifier which
operates from near DC to as high a frequency as possible. Much more amplifier design
material will be covered later. Let us use the somewhat simpler transistor model below.
Again, gm=100 mS, Cgs=0.32 pF, and Rds=200 Ohms.
Cgs
Rds
gmVgs
a) start with the network below, and simulate its 4 S-parameters. Choose a sensible
frequency range ! The shunt resistors on input and outputs form lossy matching
networks, which result in small S11 and S22 at low frequencies. What is the 3 dB
bandwidth of the amplifier ? Over what range of frequencies is S11 better than -10 dB ?
port 2
port 1
67 Ohms
50 Ohms
b) Now add a series L and Shunt C. Adjust the values so that S11 is zero (minus infinity
dB) at 20 GHz, and again plot S11 and S21 versus frequency. What have you done to the
gain-frequency response ? What is the 3-dB bandwidth of S21 and the -10 dB bandwidth
of S11 ?
2
port 2
port 1
67 Ohms
50 Ohms
c) Below is a smarter strategy. The T-section. Design by hand: Pick the value of L such
that the 2 inductors, in combination with Cgs, form a 50-Ohm T-section. Then plot again
S21 and S11. What is the 3-dB bandwidth of S21 and the -10 dB bandwidth of S11 ?
L
port 2
port 1
67 Ohms
L
50 Ohms
better still is the bridged-T (below).
L
port 2
port 1
67 Ohms
L
50 Ohms
This is based on the network below, where Z o = ( L / C )1 / 2
3
C/4
L/2
L/2
Z0
C
4