Download Two Port Characterizations Electronic Circuits 1 Contents • Input and output resistances

Electronic Circuits 1
Two Port Characterizations
Contents
• Input and output resistances
• Two port networks
• Models
Prof. C.K. Tse: 2-port networks
1
Impedances and loading effects
Voltage amplifiers
Rs
vs
+
–
Rout
+
vin
Rin
+
–
Avvin
–
smaller the better
(the best is 0)
+
vo
–
RLOAD
larger the better
(the best is ∞)
Prof. C.K. Tse: 2-port networks
2
Impedances and loading effects
Current amplifiers
larger the better
(the best is ∞)
iin
is
Rs
Rin
Aiiin
Rout
iout
RLOAD
smaller the better
(the best is 0)
Prof. C.K. Tse: 2-port networks
3
Impedances and loading effects
Transconductance amplifiers
larger the better
(the best is ∞)
Rs
vs
+
–
+
vin
–
Gmvin
Rin
Rout
iout
RLOAD
larger the better
(the best is ∞)
Prof. C.K. Tse: 2-port networks
4
Impedances and loading effects
Transresistance amplifiers
iin
is
Rs
Rout
Rin
+
–
Rmiin
smaller the better
(the best is 0)
+
vo
–
RLOAD
smaller the better
(the best is 0)
Prof. C.K. Tse: 2-port networks
5
Finding impedances
Input impedance
Inject a current to the input, find the voltage. The ratio of
the voltage to current gives the input resistance.
WITH Output
open-circuit if it is
supposed to be a voltage
output (e.g., voltage
amplifiers and
transresistance amplifiers)
ix
+
vx
–
short-circuit if it is
supposed to be a current
output (current amplifiers
and transconductance
amplifiers)
Rin
Prof. C.K. Tse: 2-port networks
6
Finding impedances
Output impedance
Inject a current at output, find the voltage. The ratio of
the voltage to current gives the output resistance.
WITH input
short-circuit if it is
supposed to be a voltage
input (e.g., voltage
amplifiers and
transconductance
amplifiers)
open-circuit if it is
supposed to be a current
input (current amplifiers
and transresistance
amplifiers)
ix
+
vx
–
Rout
Prof. C.K. Tse: 2-port networks
7
Example: CE amplifier with ED
Input resistance is
vin
iB
rin
RB1 || RB2
B
C
rπ
~
ro
gmvBE
E
+
vo
–
E
RE
rin =
=
v in v BE + v E
=
iB
iB
v BE v E
+
iB
iB
= rπ +
vE
iB
= rπ +
vE
i E /(1 + β )
= r π + (1 + β )RE
Prof. C.K. Tse: 2-port networks
8
Example: EF amplifier
B
Output resistance is
C
rπ
~
rout =
ro
im
gmvBE
E
RE
vE
=
iE +
E
rout
v m −v BE
−v BE
=
=
im
im
i E − i B − gmv BE
+
–
vm
=
vE
+ gmv E
rπ
1
1
1
+
+ gm
RE r π
1
1
≈
g
1
1
+ m + gm
+ gm
RE
RE
β
= RE ||
Prof. C.K. Tse: 2-port networks
=
1
gm
9
Quick rule 1
r π + (1 + β )RE
RE
Prof. C.K. Tse: 2-port networks
10
Example
r π + (1 + β )[RE 1 || (r π + (1 + β )RE 2 )]
RE1
RE2
Prof. C.K. Tse: 2-port networks
11
Quick rule 2
RB
RB
RB
1
+
gm 1 + β
RE
Prof. C.K. Tse: 2-port networks
 1
RB 


+
 gm 1 + β 
RE
12
Example
RL
RB
RE
 1
RL + RB 


+
1+ β 
 gm
Prof. C.K. Tse: 2-port networks
RE
13
General two port characterizations
2
1
i1
i2
+
v2
–
+
v1
–
Prof. C.K. Tse: 2-port networks
14
Types of characterizations
Immittance parameters
- z-parameters
- y-parameters
Hybrid parameters
- h-parameters
- g-parameters
Prof. C.K. Tse: 2-port networks
15
z-parameters
i1
+
v1
–
1
2
i2
+
v2
–
v  z
z i 
 1  =  11 12  1 
v 2  z 21 z 22 i 2 
z11 =
v1
i1 i
v1
i2 i
z12 =
z 21 =
2 =0
1 =0
(open-circuit port 2)
(open-circuit port 1)
v2
i1
i1 =0 (open-circuit port 2)
v2
i2
i 2 =0 (open-circuit port 2)
z 22 =
Prof. C.K. Tse: 2-port networks
16
y-parameters
i1
+
v1
–
1
2
i  y
y 12 v 1 
1
11
 =
 
i 2  y 21 y 22 v 2 
i2
+
v2
–
y 11 =
y 12 =
y 21 =
y 22 =
Prof. C.K. Tse: 2-port networks
i1
v1 v
2 =0
(short-circuit port 2)
i1
v2 v
1 =0
(short-circuit port 1)
i2
v1 v
1 =0
(short-circuit port 2)
i2
v2 v
2 =0
(short-circuit port 2)
17
h-parameters
i1
1
2
v  h
h12  i1 
1
11
 =
 
i 2  h21 h22 v 2 
i2
+
v1
–
+
v2
–
h11 =
h12 =
BJT model in some books:
h11 = rπ
input resistance
h21 = hfe = β
Early resistance
h22 = 1/ro
h21 =
h22 =
Prof. C.K. Tse: 2-port networks
v1
i1 v
v1
v2
i2
i1 v
i2
v2
2 =0
(short-circuit port 2)
i1 =0 (open-circuit port 1)
2 =0
(short-circuit port 2)
i1 =0 (open-circuit port 1)
18
g-parameters
i1
+
v1
–
1
2
 i  g
g12 v 1
1
11
 =
 
v 2  g21 g22 i 2 
i2
+
v2
–
g11 =
g12 =
i1
v1 i
2 =0
i1
i2 v
1 =0
g21 =
g22 =
v2
v1
(open-circuit port 2)
(short-circuit port 1)
i 2 =0 (open-circuit port 2)
v2
i2 v
1 =0
Prof. C.K. Tse: 2-port networks
(short-circuit port 1)
19
Example
i1
+
v1
–
R1
R2
i2
+
v2
–
h11 =
v1
i1 v
h12 =
h21 =
h22 =
Prof. C.K. Tse: 2-port networks
v1
v2
i2
i1 v
i2
v2
= R1 || R2 =
2 =0
=
R2
R1 + R2
=
−R2
R1 + R2
=
1
R1 + R2
i 1 =0
2 =0
i 1 =0
R1R2
R1 + R2
20
Connecting two-ports — series-series
i1
+
v1
–
i2
Z
i3
+
v3
–
+
v2
–
i4
Z’
+
v4
–
Total [Z]T = [Z]+[Z’]
Prof. C.K. Tse: 2-port networks
21
Connecting two-ports — shunt-shunt
i1
+
v1
–
i2
Y
i3
+
v3
–
+
v2
–
i4
Y’
+
v4
–
Total [Y]T = [Y] + [Y’]
Prof. C.K. Tse: 2-port networks
22
Connecting two-ports — shunt-series
i1
+
v1
–
i2
G
i3
+
v3
–
+
v2
–
i4
G’
+
v4
–
Total [G]T = [G] + [G’]
Prof. C.K. Tse: 2-port networks
23
Connecting two-ports — series-shunt
i1
+
v1
–
i2
H
i3
+
v3
–
+
v2
–
i4
H’
+
v4
–
Total [H]T = [H] + [H’]
Prof. C.K. Tse: 2-port networks
24
Circuit models
We can develop circuit model for each type of two-port descriptions.
Example: h-parameter
v  h
v = h i + h v
h12  i1 
1
11
11 1
12 2
 =
  ⇒  1
i 2 = h21i1 + h22v 2
i 2  h21 h22 v 2 
i1
+
v1
–
i2
h11
1/h22
+
–
h12v2
h21i1
Prof. C.K. Tse: 2-port networks
+
v2
–
25
Example: BJT model
We can model the BJT as a h-parameter model:
h11 = rπ
input resistance
h12 ≈ 0
h21 = hfe = β
h22 = 1/ro
Early resistance
i1
+
v1
–
i2
rπ
βi1
= gmv1
Prof. C.K. Tse: 2-port networks
ro
+
v2
–
26