Lecture 15

FET Small AC Signal Model

FET Small AC Signal Model 1-1

OutlineSmall AC Signal Equivalent Circuits for FETs Amplifier Circuits Examples

Introduction to Power Electronics Power Semiconductor Devices

• Power MOSFET

FET Small AC Signal Model 1-2

FET Small-Signal Model

Transconductance

The relationship of a change in ID to the corresponding

change in VGS is called transconductance or mutual

conductance

Transconductance is denoted gm and given by:

Device transconductance, gm, is provided on

specification sheets as forward transfer admittance, yfs

FET Small AC Signal Model 1-3

GS

Dm

V∆

I∆g =

Graphical Determination of gm

FET Small AC Signal Model 1-4

Mathematical Definitions of gm

FET Small AC Signal Model 1-5

GS

Dm

V

Ig

∆∆∆∆

∆∆∆∆====

−=

P

GS

P

DSSm

V

V1

V

2Ig

P

DSSm0

V

2Ig ====

−−−−====

P

GSm0m

V

V1gg

DSS

D

P

GS

I

I

V

V1 ====−−−−

DSS

Dm0

P

GSm0m

I

Ig

V

V1gg ====

−−−−====

Where VGS =0V

Where

For JFET and Depletion Type MOSFET

Mathematical Definitions of gm For Enhancement Type MOSFET

FET Small AC Signal Model 1-6

GS

Dm

V

Ig

∆∆∆∆

∆∆∆∆====

K

I)VV( D

TGS =−

DD

m I2K

I2Kg K==

Where

[ ]2

TGSD VVKI −=

[ ]TGSm VVK2g −=

FET AC Equivalent Circuit

FET Small AC Signal Model 1-7

Ω∞= Zi

osdo

y

1rZ ========

constant VD

DSd GSI

Vr ========

∆∆∆∆

∆∆∆∆

Input impedance:

Output Impedance:

where:

yos= output admittance parameter listed on FET specification sheets.

Common-Source (CS) Fixed-Bias Circuit

FET Small AC Signal Model 1-8

Gi RZ ====

dDo r||RZ ====

10RrDo

Dd

RZ≥≥≥≥

≅≅≅≅

Input impedance:

Output impedance:

)R||(rgV

VA Ddm

i

ov −−−−========

Dd 10RrDmi

ov Rg

V

VA

≥≥≥≥−−−−========

Voltage gain:

1G

off-cutCR.2

1f

π=

Coupling

capacitors

2D

off-cutCR.2

1f

π=

Common-Source (CS) Voltage-Divider Bias

FET Small AC Signal Model 1-9

21i R||RZ ====

Ddo R||rZ ====

10RrDo

Dd

RZ≥≥≥≥

≅≅≅≅

Input impedance:

Output impedance:

)R||(rgA Ddmv −−−−====

Dd 10RrDmv RgA

≥−=

Voltage gain:

Common-Gate (CG) Circuit

The input is on the source and the output is on the drain

There is no phase shift between input and output

FET Small AC Signal Model 1-10

Calculations

FET Small AC Signal Model 1-11

Input impedance:

Output impedance:

=

−=

−=

=

m

Si

i

i

g

1||RZ

I

Z

igs

gsm

s

i

i

i

vv

vgR

v

I

v

Do RZ ≅

Dm

gs

Dgsm

i

DgsmRg

v

Rvg

v

Rvg=

−

−=

−==

i

ov

V

VA

Voltage gain:

Dd 10Rr ≥

Example (1)

FET Small AC Signal Model 1-12

The fixed-bias configuration had an operating point defined by VGSQ = - 2 V and IDQ = 5.625 mA, with IDSS = 10 mA and VP = -8 V. The value of yos is provided as 40 µS.

(a) Determine gm.

(b) Find rd.

(c) Determine Zi.

(d) Calculate Zo.

(e) Determine the voltage gain Av.

Example (1) – Solution

FET Small AC Signal Model 1-13

Small AC Signal Equivalent Model for MOSFET

- The ac equivalent model for MOSFETs is exactly the same as that employed for JFETs

- The only difference offered by D-MOSFETs is that VGSQ can be positive for n-channel devices and negative for p-channel units

- The result is that gm can be greater than gm0

FET Small AC Signal Model 1-14

Common-Source Drain-Feedback

There is a 180° phase shift between input and output

FET Small AC Signal Model 1-15

Calculations

FET Small AC Signal Model 1-16

Input impedance:

Output impedance:)R||(rg1

R||rRZ

)R||rR(I)R||rg1(v

R||)rvgI(RIv

vgII

R||rIRIv

I

vZ

Ddm

DdFi

DdFiDdmi

DdgsmiFii

gsmiR

DdRFii

i

ii

+

+=

+=+

−+=

−=

+=

=

DdFo ||Rr||RZ ====

DdDdF 10Rr,R||rRDo RZ ≥≥≥≥>>>>>>>>≅≅≅≅

)R||r||(RgA DdFmv −=

Dmv D10Rdr,DR||drFRRgA ≥>>−≅

Voltage gain:

Power Electronics Technology

Power electronics is the application of solid-state (e.g., crystalline semiconductor) electronics for the control and conversion of electric power

The potential for applications of power electronics become wider used in a great variety of high power product, including heat

controls, light controls, electric motor control, power supplies, vehicle propulsion system and high voltage direct current (HVDC) systems

Many power semiconductor devices (e.g., power MOSFET) are available and directed to the field of power electronics A power semiconductor device is an electronic device that can

be used as switches in power electronic circuits FET Small AC Signal Model 1-17

Power Electronics Application

FET Small AC Signal Model 1-18

Power Electronics Technology

Switching and signal conversion applications using the power semiconductor devices (or power electronic converter) fall generally into six categories : AC to DC Converter (Controlled Rectifier)

DC to DC Converter (DC Chopper)

AC to AC Converter (AC voltage regulator)

DC to AC Converter (Inverter)

Static Switches

Developing power electronic converter circuits requires designing power and control circuits

FET Small AC Signal Model 1-19

Power Semiconductor Devices

Interesting parameters Breakdown voltage

On-resistance

Rise and fall times

Safe operating area

Thermal resistance

Different power transistors BJT (Bipolar Junction Transistor)

MOSFET (Metal Oxide Semiconductor Field effect transistor)

IGBT (Insulated Gate Bipolar Transistor) FET Small AC Signal Model 1-20

Classification of Power Semiconductor Devices

FET Small AC Signal Model 1-21

using both majority and minority carriers (i.e., electrons and electron holes)

Using only one type of charge carriers

Power MOSFET

Vertical diffused MOS (VDMOS) or Double-Diffused MOS (or simply DMOS) Structure

designed tohandle significantpower levels

high current commutationspeed and good efficiency at low voltages

found in most power supplies, DC to DC converters, and low voltage motor controllers

FET Small AC Signal Model 1-22

MOSFET/IGBT Switch

FET Small AC Signal Model 1-23

IGBT has lower switching speed than power MOSFET

Comparisons between MOSFETs and BJTs

FET Small AC Signal Model 1-24

MOSFETs BJTs

Pros Cons

High input impedance Low input impedance

Minimal drive power, no DC current required at gate

Large drive power, continuous DC current required at base

Simple drive circuits Complex drive circuits as large +ve and –vecurrents areinvolved

Devices can be easily paralleled Devices cannot be easily paralleled

Max. operating temp. ~ 200 oC Max. operating temp. ~ 150 oC

Very low switching losses Medium to high switching losses (depends on trade-off with conduction losses)

High switching speed, less temp. sensitive Lower switching speed, more sensitive to temp

Cons Pros

High on-resistance Low on-resistance

Low transconductance High transconductance

Lecture-related Question

Design the fixed-bias circuit to have an AC gain of 10

FET Small AC Signal Model 1-25

Solution

FET Small AC Signal Model 1-26

Lecture Summary

Covered material

Small AC Signal Equivalent Circuits for FETs Amplifier Circuits Examples

Introduction to Power Electronics Power Semiconductor Devices

• Power MOSFET

Material to be covered next lecture

Complementary metal–oxide–semiconductor (CMOS) Inverting circuits