Mathcad - ee217projtodonew2.mcd

Small Signal Analysis
A small signal analysis of the network is necessary for noise, gain, and impedance matching
calculations. Kirkoff’s Current Laws (KCL) were used to set up a general purpose matrix to solve
for the necessary gains. The following figure was used perform the small signal analysis.
C µ
Z S
r b
i bn I cn R L
V S
Z π
g m *v π
Z bias
Z L
v nRbias
Z e
v nRL
Fig. 6: Small Signal Model of LNA Circuit
KCL at bias node, V bias
V S
V bias V bias V nbias V bias V b
Z S Z bias r b
V S
Z S
V bias
Z S
V bias V bias V b
Z bias r b
KCL at base node, V b
V bias V b
V b V . c j. ω . C µ
r b
KCL at collector node, V c
V b V . c j. ω . C µ g . m V b V e
V b V e
V b
0
Z π
V c
r o
V e
V c
R L
V c V L
Z L
V bias
V b V . c j. ω . C µ
r b
V . c j. ω . C cs
V b
Z π
V e
V L
V c V . b j. ω . C µ g . m V b V e
Z L
V c
r o
V e
V c
R L
V c
Z L
V . c j. ω . C cs
KCL at emitter node, V e
V b V e
g . m V b V e
Z π
V c
r o
V e
V e
Z e
0
These KCL equations are now placed into a KCL matrix
V S
Z S
0
V L
Z L
0
1 1 1
Z S Z bias r b
1
r b
0
0
V e V e V b
g . m V e V b
Z e Z π
1
0
0
r b
1
j. ω . 1
C µ
j. ω .
1
C µ
r b
Z π
Z π
j. ω . C µ g m j. ω . 1 1
1
C µ
g m
Z L r o
r o
1
1 1 1 1
g m g m
Z π r o Z e Z π r o
Note that these equations don’t have R L in them. The necessary R L will be calculated later in the
stability section.
.
V bias
V b
V c
V e
V e
r o
V c