1. Chapter 13 Small-Signal Modeling and Linear Amplification
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
Microelectronic Circuit Design, 3E
McGraw-Hill

2. Microelectronic Circuit Design, 3E
dc and ac Analysis
DC analysis:
Find dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits.
Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model.
AC analysis:
Find ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits.
Replace transistor by small-signal model
Use small-signal ac equivalent to analyze ac characteristics of amplifier.
Combine end results of dc and ac analysis to yield total voltages and currents in the network.
Microelectronic Circuit Design, 3E
McGraw-Hill

3. dc Equivalent for BJT Amplifier
All capacitors in original amplifier circuits are replaced by open circuits, disconnecting vI , RI , and R3 from circuit.
Microelectronic Circuit Design, 3E
McGraw-Hill

4. ac Equivalent for BJT Amplifier
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

5. DC and AC Equivalents for MOSFET Amplifier
dc equivalent
Full circuit
ac equivalent
Simplified ac equivalent
Microelectronic Circuit Design, 3E
McGraw-Hill

6. Small-Signal Operation of Diode
The slope of the diode characteristic at the Q-point is called the diode conductance and is given by:
gd is small but non-zero for ID = 0 because slope of diode equation is nonzero at the origin.
Diode resistance is given by:
Microelectronic Circuit Design, 3E
McGraw-Hill

7. Small-Signal Operation of Diode (cont.)
Subtracting ID from both sides of the equation,
For id to be a linear function of signal voltage vd ,
This represents the requirement for small-signal operation of the diode.
Microelectronic Circuit Design, 3E
McGraw-Hill

8. Current-Controlled Attenuator
Magnitude of ac voltage vo developed across diode can be controlled by value of dc bias current applied to diode.
From ac equivalent circuit,
From dc equivalent circuit ID = I,
For RI = 1 kW, IS = A,
If I = 0, vo = vi, magnitude of vi is limited to only 5 mV.
If I = 100 mA, input signal is attenuated by a factor of 5, and vi can have a magnitude of 25 mV.
Microelectronic Circuit Design, 3E
McGraw-Hill

9. Small-Signal Model of BJT
Using 2-port y-parameter network,
The port variables can represent either time-varying part of total voltages and currents or small changes in them away from Q-point values.
bo is the small-signal common-emitter current gain of the BJT.
Microelectronic Circuit Design, 3E
McGraw-Hill

10. Microelectronic Circuit Design, 3E
Hybrid-Pi Model of BJT
Transconductance:
Input resistance:
The hybrid-pi small-signal model is the intrinsic representation of the BJT.
Small-signal parameters are controlled by the Q-point and are independent of geometry of the BJT
Output resistance:
Microelectronic Circuit Design, 3E
McGraw-Hill

11. Small-Signal Current Gain and Amplification Factor of BJT
Amplification factor is given by:
For VCE << VA,
mF represents maximum voltage gain individual BJT can provide and doesn’t change with operating point.
bo > bF for iC < IM , and bo < bF for iC > IM , however, bF and bo are assumed to be equal.
Microelectronic Circuit Design, 3E
McGraw-Hill

12. Equivalent Forms of Small-Signal Model for BJT
Voltage -controlled current source gmvbe can be transformed into current-controlled current source,
Basic relationship ic = bib is useful in both dc and ac analysis when BJT is in forward-active region.
Microelectronic Circuit Design, 3E
McGraw-Hill

13. Small-Signal Model for the MOSFET
Using 2-port y-parameter network,
The port variables can represent either time-varying part of total voltages and currents or small changes in them away from Q-point values.
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

14. Small-Signal Parameters of MOSFET
Transconductance:
Output resistance:
Since gate is insulated from channel by gate-oxide input resistance of transistor is infinite.
Small-signal parameters are controlled by the Q-point.
For same operating point, MOSFET has higher transconductance and lower output resistance that BJT.
Amplification factor for lVDS<<1:
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

15. Small-Signal Operation of MOSFET
For linearity, id should be proportional to vgs:
Since the MOSFET can be biased with (VGS - VTN) equal to several volts, it can handle much larger values of vgs than corresponding the values of vbe for the BJT.
Change in drain current that corresponds to small-signal operation is:
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

16. Small-Signal Model for PMOS Transistor
Positive signal voltage vgg reduces source-gate voltage of the PMOS transistor causing decrease in total current exiting drain, equivalent to an increase in the signal current entering the drain.
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

17. Small-Signal Analysis of Complete C-S Amplifier: ac Equivalent
ac equivalent circuit is constructed by assuming that all capacitances have zero impedance at signal frequency and dc voltage sources represent ac grounds.
Assume that Q-point is already known.
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

18. Microelectronic Circuit Design, 3E
Small-Signal Analysis of Complete CS Amplifier: Small-Signal Equivalent
Noting similarity to CE case, Terminal voltage gain between gate and drain is found as:
With r infinite, RiG is also infinite, therefore overall voltage gain from source vi to output voltage across RL is:
Jaeger/Blalock
7/20/07
Microelectronic Circuit Design, 3E
McGraw-Hill

19. C-S Amplifier Voltage Gain: Example
Problem: Calculate voltage gain
Given data: Kn = 0.5 mA/V2, VTN = 1V, l= V-1, Q-point is (1.45 mA, 3.86 V), R1 = 430 kW, R2 = 560 kW, R3 = 100 kW, RD = 4.3 kW, RI = 1 kW.
Assumptions: Transistor is in active region. Signals are low enough to be considered small signals.
Analysis:
Microelectronic Circuit Design, 3E
McGraw-Hill