Microwave Integrated Circuits
Professor Jayanta Mukherjee
Department of Electrical Engineering
Indian Institute of Technology Bombay
Module 7
Lecture No 28
Gain Circles (contd.)
Hello, welcome to another module of this course, microwave integrated circuits. In the previous
module, we are in week 7 now. In the 1
st
module of week 7, we had covered about design using
the gain circle for the unilateral phase using the transducer gain as our specification for the gain.
And then we had seen what we had also discussed about the unilateral figure of merit to show
how good an approximation, the unilateral approximation was. I had also mentioned in the
previous module that next we will be covering the bilateral case. That is the case when we do not
make the unilateral approximation. So let us see how, what we can actually do.
Now one thing I would like to state for the bilateral phase is that unlike the unilateral case there
is not much design flexibility. I mean what we can achieve mathematically is to specify the
maximum gain that we can get unlike the unilateral approximation case where you could specify
a particular gain and then draw a load side and source side gain circle. In the bilateral case, we
cannot do that.
(Refer Slide Time:
1:39)
Now if the device unconditionally stable that is A greater than 1 and B greater than 0 or Delta
less than 1 then for conjugate maths, we have to have and gamma L should be equal to now we

know what is the equation for gamma in and the equation for gamma out and if we solve these 3
equations simultaneously then the solution that we will get is given like this.
2
2
1
1
1
1
2
2
2
2
2
2
2
2
2
1
11
22
2
2
2
2
22
11
*
1
11
22
*
2
22
11
4
2
4
2
1
1
MS
MS
B
B
C
C
B
B
C
C
where
B
S
S
B
S
S
C
S
S
C
S
S
Where th
is B1, Bs and Cs are given by…
Now if we substitute these values into the gain equation then the value of gain we call the
gaming question for the non-unilateral case that is when we do not make that is when S12 is not
equal to 0. I’m not repeating that equation but if we substitute these values of gamma S and
gamma ML in that equation, what we get is actually the maximum possible game, maximum
possible value of GT for the bilateral case. And that value of GT, that maximum value of GT that
we get is given by
…

(Refer Slide Time:
4:56)
2
21
max
12
max
max
max
21
21
21
max
2
12
12
12
1
1
1
T
T
P
A
T
S
G
K
K
S
G
G
G
S
y
z
G
S
y
z
K
K
Now we can show, we have already talked about GP that is the power gain or the operating
power gain and GA is the available power gain. Now we can show that GT Max will be equal to
GP Max which is equal to GA Max. Now this can also be simplified like this. Now just dividing
the numerator and denominator by K+ square root of K square -1, what we will get is this. This
S21 upon S12 is equal to any of the values. That is this is also equal to Y21 upon Y12. You can
verify that from the conversion formulas for between Z and S parameters. Now, we saw that this
is the case for the unconditionally stable case.

max