DESIGN
In ECE145A/ECE218A
AMPLIFIER other courses, you have learned to design amplifiers using small signal models for devices. This works reasonably well at lower frequencies, but at high frequencies often the device S.S. model is not accurate enough. Then, measured s-parameters can be used to accurately design the amplifier. The s-parameter design technique employs relationships between input and output powers, forward and reflected powers that look scary at first but can easily be derived using the signal flow graph method and Mason's gain rules. (Gonzalez, Sec. 2.6) Our sequence of topics will include: 1. Signal flow graph method (homework) 2. Power gain definitions 3. Stability of amplifiers 4. Unilateral approximation ( S12 =0) 5. Bilateral design 6. Bias circuits and wideband stability
Goal: Learn to design stable narrowband amplifiers using S parameters
12/14/07
1
Prof. Stephen Long, ECE/UCSB
ECE145A/ECE218A
Recall the definition of the S parameters:
AMPLIFIER DESIGN
b1 = S11a1 + S12 a2 b2 = S21a1 + S 22 a2
a1 b1 S A transistor
a2 b2
Consider the forward transmission and calculate the transducer power gain:
S 21 =
In general, for an arbitrary RS and RL,
2Vout b2 = Vgen a1
a2 =0
PAVS =
2 Vgen
8 RS
PL =
2 Vout 2 RL
The definition of transducer power gain:
GT =
So, for the special case where RS = RL = ZO,
PL PAVS
2 2 4Vout Vout 8Z O = GT | S21 | = 2 = 2 Vgen 2 Z O Vgen 2
12/14/07
2
Prof. Stephen Long, ECE/UCSB
ECE145A/ECE218A
AMPLIFIER DESIGN
But, life is generally not that straightforward because |S21|2 is often much less than the optimum gain that you could obtain from a given transistor. You must add matching networks to transform ZO to a more suitable S and L. AMPLIFIER BLOCK DIAGRAM
in
out
Z1 = 50
input MN
output MN
Z2 = 50
S
L
How do we calculate gain from s-parameters? Evaluate the appropriate gain equation:
GT = transducer power gain = PL PAVS 1- L
2 2
=
1- S
2 2
1 - S11S
S21
2
1 - out L
gain term associated with input match
GT of device if S = L = 0
gain term associated with output match
where out = S22 +
S12 S21S 1 - S11S
So, if you are given the S params and S ,L then you can calculate the gain. Note however that out depends on S unless S12 = 0!
12/14/07
3
Prof. Stephen Long, ECE/UCSB
ECE145A/ECE218A Why does OUT depend on S?
AMPLIFIER DESIGN
b1 = S11a1 + S12 a2 b2 = S21a1 + S22 a2
But, a1 = sb1 . Substitute into the equation for b1
b1 = S11 sb1 + S12a2 b1 (1 - S11 s ) = S12a2
or
b1 = OUT = b2 a2
S12a2 (1 - S11 s )
Now, find
S S b2 = 21 s 12 + S22 a2 (1 - S11 s ) S S OUT = 21 s 12 + S22 (1 - S11 s ) S S IN = 21 L 12 + S11 (1 - S22 L )
So, an amplifier is truly unilateral only when S12 = 0
Thus, Likewise,
12/14/07
4
Prof. Stephen Long, ECE/UCSB
ECE145A/ECE218A
AMPLIFIER DES...
ampdesign