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Lecture 16: Small Signal Amplifiers. Prof. Niknejad. Lecture Outline. Review: Small Signal Analysis Two Port Circuits Voltage Amplifiers Current Amplifiers Transconductance Amps Transresistance Amps Example: MOS Amp Again!. Small Signal Analysis. - PowerPoint PPT Presentation
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Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16
Lecture 16:
Small Signal Amplifiers
Prof. Niknejad
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Lecture Outline
Review: Small Signal Analysis Two Port Circuits
– Voltage Amplifiers– Current Amplifiers– Transconductance Amps– Transresistance Amps
Example: MOS Amp Again!
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small Signal Analysis
Step 1: Find DC operating point. Calculate
(estimate) the DC voltages and currents (ignore
small signals sources)
Substitute the small-signal model of the
MOSFET/BJT/Diode and the small-signal models
of the other circuit elements.
Solve for desired parameters (gain, input
impedance, …)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
A Simple Circuit: An MOS Amplifier
DSI
GSV
sv
DR DDV
GS GS sv V v
ov
Input signal
Output signal
Supply “Rail”
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small-Signal Analysis
Step 1. Find DC Bias – ignore small-signal source
VGS,BIAS was found inLecture 15
IGS,Q
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small-Signal Modeling
What are the small-signal models of the DC supplies?
Shorts!
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small-Signal Models of Ideal Supplies
Small-signal model:
supplysupply
supply
ig
v
supply 0r
supplysupply
supply
0i
gv
supplyr
short
open
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small-Signal Circuit for Amplifier
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Low-Frequency Voltage Gain
Consider first 0 case … capacitors are open-circuits
Transconductance
,2( ) D SAT
m n ox GS TGS T
IWg C V V
L V V
||out m s D ov g v R r
||v m D oA g R r
Design Variable
Design Variables
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Voltage Gain (Cont.)
Substitute transconductance:
Output resistance: typical value n= 0.05 V-1
,
1 1200k
0.05 0.1on D SAT
r kI
Voltage gain: 2 0.125 || 200 14.3
0.32vA
,2||D SAT
v D oGS T
IA R r
V V
m Dg R
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Input and Output Waveforms
Output small-signal voltage amplitude: 14 x 25 mV = 350
Input small-signal voltage amplitude: 25 mV
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
What Limits the Output Amplitude?
1. vOUT(t) reaches VSUP or 0 … or
2. MOSFET leaves constant-current region and enters triode region
, 0.31VDS DS SAT GS TnV V V V
, , 0.32Vo MIN DS SATv V
2.5 0.32V = 2.18Vamp
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Maximum Output Amplitude
vout(t)= -2.18 V cos(t) vs(t) = 152 mV cos(t)
How accurate is the small-signal (linear) model?
0.1520.5
0.32s
GS Tn
v
V V
Significant error in neglecting third term in expansion of iD = iD (vGS)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Generalized Amplifier
sv S BIAS sv V v
ov
BIASV
DDV
SSVBIASIsi
SR
DDIL DD Di I i
( )D ini f vLR
inv
Active Device
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Amplifier Terminology
Sources: Signal, its source resistance, and bias voltage or current
Load: Use resistor in Chap. 8, but could be a general impedance
Port: A pair of terminals across which a voltage and an associated current are defined
Source, Load: “one port” Amplifier: “two port”
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
One-Port Models (EECS 40)
A terminal pair across which a voltage and associated current are defined
CircuitBlockabv
abi
thevv
thevR
abv
abi
thevithevRabv
abi
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small-Signal Two-Port Models
We assume that input port is linear and that the amplifier is unilateral: – Output depends on input but input is independent of
output. Output port : depends linearly on the current and
voltage at the input and output ports Unilateral assumption is good as long as “overlap”
capacitance is small (MOS)
inv
outv
outiini
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Math 54 Perspective
Can write linear system of equations for either iout or vout
in terms of two of iin, vin, iout, or vout: possibilities are
1 2out in outi v v
3 4out in outi i v
5 6out in outv v i
7 8out in outv i i
What is physical meaning of 1? of 6?
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
EE Perspective
Four amplifier types: determined by the output signal and the input signal … both of which we select (usually obvious)– Voltage Amp (VV)– Current Amp (II)– Transconductance Amp (VI)– Transresistance Amp (IV)
We need methods to find the 6 parameters for the four models and equivalent circuits for unilateral two ports
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Two-Port Small-Signal Amplifiers
si sR inR outR LRi inAi
ini
sv
sR
inR
outR
LRv inA vinv
Current Amplifier
Voltage Amplifier
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Two-Port Small-Signal Amplifiers
sv
sR
inRoutR LRm inG v
inv
si sR inR
outR
LRm inR i
ini
Transresistance Amplifier
Transconductance Amplifier
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Input Resistance Rin
Looks like a Thevenin resistance measurement, but note that theoutput port has the load resistance attached
attachedRremovedRt
tin
LSi
vR
,
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Output Resistance Rout
Looks like a Thevenin resistance measurement, but note that theinput port has the source resistance attached
attachedRremovedRt
tout
SLi
vR
,
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Finding the Voltage Gain Av
Key idea: the output port is open-circuited and the source resistance is shorted
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Finding the Current Gain Ai
Key idea: the output port is shorted and the source resistance is removed
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Finding the Transresistance Rm
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Finding the Transconductance Gm
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Common-Source Amplifier (again)
How to isolate DC level?
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
DC Bias
Neglect all AC signals
5 V
2.5 V
Choose IBIAS, W/L
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Load-Line Analysis to find Q
Q
D
DD outR
D
V VI
R
1
10kslope
0V
10kDI
5V
10kDI
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Small-Signal Analysis
inR
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
sv
sR
inRoutR LRm inG v
inv
Two-Port Parameters:
Find Rin, Rout, Gm
inR
m mG g ||out o DR r R
Generic Transconductance Amp
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 16 Prof. A. Niknejad
Two-Port CS Model
Reattach source and load one-ports:
