Introduction to RF Active Devices

RF Electronics Spring, 2020

Robert R. Krchnavek Rowan University

Objectives

• Understand various high-frequency circuit models for diodes, BJTs. (FETs on your own from text.)

• Understand the difference between large-signal and small-signal models.

• Where possible, link the model to device physics at the level explored in Electronics I.

Large-Signal vs Small-Signal

• Diodes and transistors are nonlinear devices.

• Large-signal models are more closely based on the physics of the devices than small-signal models.

• The large-signal model must consider the nonlinear nature of the device.

• Over a small signal range, we can “linearize” the device and create a small-signal model.

• Large-signal models are usually used to determine bias conditions whereas small-signal models are used to determine signal flow.

Diode Models Large-Signal or Nonlinear Model

ID = IS

≥eVA/(nVT ) ° 1

¥

V = RSID + nVT ln (1 + ID/IS)

Diode Models Large-Signal or Nonlinear Model

C = Cd + CJ

CJ =

( CJ0(1°VA/Vdiff )m , VA ∑ Vm

CJ0(1°Vm/Vdiff )m

≥1 + m VA°Vm

Vdiff°Vm

¥, VA ∏ Vm

Cd =

dQd

dVA=

ISτT

nVTeVA/(nVT )

Diode Models Large-Signal or Nonlinear Model

IS(T ) = IS(T0)

µT

T0

∂pt/n

exp

∑°Wg(T )

VT

µ1° T

T0

∂∏

Wg(T ) = Wg(0) −

(

αT T 2

βT + T

)

Diode Models Large-Signal or Nonlinear Model

Symbol SPICE Description Typical Values

IS IS saturation current 1 fA - 10 µA

n N emission coefficient 1

τT TT transit time 5 ps - 500 µs

RS RS ohmic resistance 0.1 - 20 Ω

Vdiff VJ barrier voltage 0.6-0.8 V (pn) 0.5-0.6 V (Schottky)

CJ0 CJ0 zero-bias junction capacitance 5-50 pF (pn) 0.2-5 pF (Schottky)

m M grading coefficient 0.2-0.5

Wg EG bandgap energy 1.11 eV (Si) 0.69 eV (Si-Schottky)

pt XTI saturation current temperature coefficient

3 (pn) 2 (Schottky)

Diode Models Small-Signal or Linear Model

Diode Models Small-Signal or Linear Model

Gd =1

Rd=

dID

dVA

ØØØØVQ

=IQ + IS

nVTº IQ

nVT

Cd =ISøT

nVTeVQ/(nVT )

Diodes at RF Frequencies

• PN - junction capacitance is usually too high for RF or MW work.

• Schottky - smaller junction capacitance makes them widely used in RF and MW work.

• PIN - often used as a variable resistor or high-frequency switch.

• varactor - PIN diode used as a variable capacitance when reverse biased.

• IMPATT, tunnel, TRAPATT, BARRIT, Gunn.

Transistors BJTs vs FETs

• Advantages of BJTs

• Generally larger gains.

• Lower input impedance (matching is easier).

• Larger power handling capabilities.

• Disadvantages of BJTs

• Poorer temperature behavior.

• Noise performance is worse.

Transistors BJTs vs FETs

• Disadvantages of BJTs (continued)

• Lower input impedance loads input stages.

• Less linear collector current behavior.

• Lower upper frequency limit.

• Consumes more power.

BJT Models Large-Signal or Nonlinear Model

• Ebers-Moll model

• Developed in Dec., 1954.

• Not the most sophisticated, but very popular.

BJT Models Large-Signal or Nonlinear Model

IE = αRIR − IF

IC = αF IF − IR

IR = ICS

(

eVBC/VT

− 1

)

IF = IES

(

eVBE/VT

− 1

)

αF IES = αRICS = IS

Forward Active Region:

VCE > VCEsat = 0.1 V

VBE ≈ 0.7 V

Reverse Active Region:

VCE < −0.1 V

VBC ≈ 0.7 V

BJT Models Large-Signal or Nonlinear Model

Adding junction capacitances, lead resistance and lead inductance, and terminal capacitance yields

BJT Models Large-Signal or Nonlinear Model

• The Ebers-Moll model cannot satisfactorily model all physical phenomena seen in actual transistors.

• βF and βR are current dependent.

• IS is affected by VBC (Early effect).

• The Gummel-Poon model fixes this.

• The SPICE model is a modified version of the Ebers-Moll model. See Example 7-2. One can also use the Gummel-Poon model.

BJT Models Small-Signal or Linear Model

We can obtain a small-signal model from the large-signal Ebers-Moll model.

BJT Models Small-Signal or Linear Model

We can obtain a small-signal model from the large-signal Ebers-Moll model.

BJT Models Small-Signal or Linear Model

We can obtain a small-signal model from the large-signal Ebers-Moll model.

BJT Models Small-Signal or Linear Model

IC = IQC +ic = IS exp

[(

V QBE + vbe

)

/VT

]

= IQC

[

1 +

(

vbe

VT

)

+1

2

(

vbe

VT

)2

+ · · ·

]

VBE = VQBE + vbe

ic =

(

IQC

VT

)

vbe = gmvbe

To create a linear model, only use the linear term in the Taylor series expansion

BJT Models Small-Signal or Linear Model

gm =

dIC

dVBE

∣

∣

∣

∣

Q

=

d

dVBEISe(VBE/VT )

∣

∣

∣

∣

Q

≈

IQC

VT

βF |Q =

dIC

dIB

∣

∣

∣

∣

Q

= β0

rπ =

dVBE

dIB

∣

∣

∣

∣

Q

=

dIC

dIB

∣

∣

∣

∣

Q

dVBE

dIC

∣

∣

∣

∣

Q

=

β0

gm

1

r0=

dIC

dVCE

∣

∣

∣

∣

Q

=d

dVCE

(

ISe(VBE/VT )

[

1 +VCE

VAN

])∣

∣

∣

∣

Q

≈

IQC

VAN

Transconductance:

Small-signal current gain:

Input resistance:

Output conductance:

BJT Models Small-Signal or Linear Model

• Other models include the h-parameter model and variations.

• Miller capacitance can be placed on the input/output sides instead of Ccb (reverse-biased BC capacitance). This allows decoupling input from output. (See Example 7-3.)

• Gain-bandwidth product – important for RF.

BJT Models Small-Signal or Linear Model

Gain-Bandwidth Product

• Calculate the short-circuit current gain, hfe(𝜔).

• hfe(𝜔) = ic/ib.

BJT Models Small-Signal or Linear Model

BJT Models Biasing, Input/Output Impedances, S-

Parameters

• 3.6 V battery source

• Total amplifier current should be <10 mA.

• Assume: VCE=2V and IC=10 mA

• S-parameters for 1 MHz < f < 100GHz.

Example 7.4

Summary

• All models suffer from a common problem: it is difficult (impossible?) to directly measure each parameter value.

• In SPICE, Ebers-Moll requires 26 parameters, and Gummel-Poon requires 41 parameters.

• Manufacturers now often only give S-parameters at certain frequencies and bias conditions.