### Common Source Amplifier

```Single Stage Amplifier
• Common Source Amplifier
• Source Follower
• Common Drain
Common Source Amplifier
•
•
•
•
•
Diode Connected
Source Degeneration
W/L=35.6 um/0.6um
Small Input Signal
Amplitude of input: 2 mV (peak to peak)
Amplitude of output: 19.5 (peak to peak)
Av=9.75
Small Signal Operation
Calculation of Small Signal Gain
(Valid only for device in saturation region)
Small Signal Model
1. small signal analysis
2. the intuitive approach
Numerical Calculation
• Small Signal Gain:
– gm=2 mS
– ro=1/gds=22.288 Kohms
– RD=6 Kohms
– AV=-gm(roRD/(ro+RD))=-9.454
What if the magnitude of the
input signal is increased?
Distortion is observed when Vin swings high.
Triode Region (1)
Triode
Region
Reduction of transconductance
in the triode region
Triode Region (2)
The DC level of Vout is tied to the AV.
An increase of RD will increase AV, but at the price of pushing
the transistor closer into the triode region.
• Common Source
– NFET Implementation
– PFET Implementation
Useful when tightly controlled resistors are not available,
or physically not realizable.
Impedance:
(Body Effect ignored.)
Body Effect
Example
M1: W/L=4.62 um/0.6um
Bias Current: 100 uA
gm2=8 mS
gds2=35.43 uS
gmbs2=100.6 uS
RX=1,068 Ohms
CS Stage with Diode Connected
Not sensitive of bias
current, e.g. gm
Better linearity.
W/L_To=35.6 um/0.6um; W/L_T1=4.62 um/0.6um
Amplitude of input: 2 mV (peak to peak)
Amplitude of output: 4.447 mV (peak to peak)
Av=2.22
Design Issue
• If the bias current is fixed and the dc
Vout (VGS) is fixed, then (W/L) of the
• It maybe difficult to increase Av.
Diode Connected PFET with CS
Plot
Amplitude of input: 2 mV (peak to peak)
Amplitude of output: 15.24 mV (peak to peak)
Av=7.62
Gain Calculation
M1: W/L=6.00 um/0.6um
Bias Current: 100 uA
Current source: 75 uA
gm=2 mS
gm2=200 uS
gds2=4.69 uS
gds=44.8 uS
Av=-8.013
CS Stage with Current Source
ro2 depends on L and ID of a transistor.
|VDS2,min=VGS-Vth2| can be reduced by increasing the width of M2.
Downside: the DC output voltage is not well-defined.
Spice Example
Amplitude of input: 2 mV (peak to peak)
Amplitude of output: 62.92 mV (peak to peak)
Av=-31.44
Sensitivty
Even a slight deviation in the gate voltage of PFET is enough
to change the output voltage signficantly.
E.g. Sensitivity of output voltage around 0.6 V.
Calculation:
W/L for T2: 24.06um/0.6um
ro1=22.288 Kohm
ro2=53.20 Kohm
gm=2 mS
Av=-31.41
Ideal Vout=0.6 V
Vth2=-0.269
Vod=-0.213
Vb=717.64 mV
Disadvantage: Sensitivity to a precise Vb.
CS Stage with Source
Degeneration
• Intuition
• Small signal gain
• Output resistance
Intuition
Vin↑, ID ↑, VS ↑
Δvin is dropped across RS, thus leading to a
smoother variation of ID.
Small Signal Gain
If gmRS>>1, AV is approximately RD/RS
ДID=ДVin/RS
Effective Gm with Nonnegligible body effect
Gain By Inspection
Interpretation: The resistance at the drain
Divided by the resistance in the source path
Determination of Gain by
Inspection Example
Output Resistance
Homework: Derive the output resistance using the small
equivalent circuit
A More Intuitive Approach
Analysis
Norton Equivalent Circuit
Gain of a Degenerated Current
Source
Conductance with body effect
Output Resistance
```