Lecture 5 Radio Electronics - LTH · – The hybrid-p-model • transistor configurations ... ce =r 0 The hybrid-pmodel for ... (CB) Coupled Transistor

Johan Wernehag, EIT

Lecture 5

Radio Electronics

Johan WernehagElectrical and Information Technology

1

Lecture 5

• RF Amplifier Analysis and Design– The hybrid-p-model

• transistor configurations• amplifier classes• example of a tuned amplifier

– Two-Port Network Representation• y, z, and ABCD parameters, definition and

applications• measurement of parameters• power gain definitions• stability

– Diagnostic test

Johan Wernehag, EIT RF Amplifier Design ETIN50 - Lecture 5 2


Transistor Models

Physical model

Simplified hybrid-p-model

Rcvin Cp

Cm

rp roic

b c

e

Ib

Vout

S-Parameter model

2-porta1

b1

b2a2

S11 S22

S21

S12


Transistors

• Example: c ¢b c = 0.5pF c ¢b e = 9pF cce = 1pFr ¢b b = 10W b = 300 VA = 50V IC = 1mA

What happens when the frequency escalates from 0 to 1 GHz?

r ¢b e = rpC ¢b e = Cp

rbc = rmCbc = Cm

rce = r0

The hybrid-p model for bipolar transistors

DC:

7.8kΩ gmvb’cvbe

+

-

e

c

v ce

+

-

b

50kΩ

15MΩ

b’10Ω

+

-

50Ω

V s 1kΩ


Transistors (cont.)

1 GHz:

7.8kΩj18Ω– gmvb’e

vbe

+

- e

c

vce

+

-

j159Ω–j318Ω–b

50kΩ

15MΩ

b’10Ω

+

-

50Ω

V s 1kΩ

1 MHz:

7.8kΩj18kΩ– gmvb’e

vbe

+

-

c

vce

+

-

j159kΩ–j318kΩ–b

50kΩ

15MΩ

b’10Ω

+

-

50Ω

V s 1kΩ

e


Voltage Gain

Av

f

f3dB


Tuned Amplifiers

• Conventional design of amplifiers results in low-pass behaviour due to capacitances and this causes problems at higher frequencies

• i.e. connect an inductor in parallel to the capacitance to form a resonant circuit.The rest of the amplifier is designed by conventional low-frequency methods

• By neutralizing these capacitances the high-frequency behaviour may be improved

– with preserved bandwidth!


The Result of Neutralization

Av

Vcc

Vcc

Both amplifiers have same bandwidth, don’t let the log-scale foul you. = / = / = / = ⇒ =1/2


Example of a Tuned Amplifier

Compare tolab 3.2!

Vcc

Vin

Vout

Rc

R1

R2 R3


Rc

b

e

cCQI

in

cc

v

V

vout

A Small Signal Model for Bipolar Transistors

ic = b ib = gm vin

gm =ICQ

kTq»

ICQ

0,026AVéëê

ùûú

vid T = 290KThe model is valid at small input signals:

vin << vT = kTq » 0,026V vid T = 290K

Signal diagram

Rcvin C

C

r roic

b c

e

b

v

i i c

pp

m

out

The simplified hybrid-p-model


Common Emitter (CE) Coupled Transistor

• High voltage gain

Av = -gm Rc

• High input resistance and capacitance

Rin =b

gm= b +1( ) re Cin = Cp + 1+ Av( )Cm

• High output resistance and low output capacitance

Rout = ro / /Rc Cout » Cm

Result of the Miller theorem

Rcb

e

c

inv

v

CE

out


Common Base (CB) Coupled Transistor

• High voltage gain

Av = gm Rc

• Low input resistance and capacitance

Rin = re » 1gm

Cin = Cp

• High output resistance and low output capacitance

Rout = ro / /Rc Cout = Cm

Rc

b

e

c

in

v

v

C B

out


• High input resistance and low input capacitance

Rin = b 1gm

+Re( ) » b re+Re( ) Cin » Cm

Common Collector (CC) Coupled Transistor

• Low voltage gain

Av » 1

• Low output resistance and capacitance

Rout = re / /Re Cout » 0

Re

b

e

c

invv

CC

out


Amplifier Classes

• Class A– linear– suitable for all signals– efficiency

vBE

iC

ICQ A

• Class B– non-linear– only signals at high and constant amplitude– efficiency

B

h £ 78%

h £ 50%

• Class C– non-linear– only signals at high and constant amplitude (e.g. FM)– efficiency

C

h £ 90%

VBEQ


When the Frequency Increases Further...

• Simple neutralization is not efficient– more reactive elements affects the properties of the transistor– more elements generally affects the properties and therefore the rough

hybrid-p-model doesn’t last

• It is more important to consider power to “preserve” available performance

• Design at high frequencies by lumped components therefore utilizes two-port models such as S-parameters that more often are measured quantities than calculated...


Two-Port Network Representation

• voltage and current– z, impedance parameters – y, admittance parameters– ABCD, chain parameters– ...

2-port

i1 i2

v1 v2

• waves– S, scattering parameters– T, transmission parameters– X, large signal scattering

parameters2-port

a1b1 b2

a2

ax = incident wave

bx = reflected wave


Two-Port

2-port

i1 i2

v1 v2

• If– the two-port is linear and – port voltages and port currents are complex quantities

the small signal properties may be characterized by four complex parameters

– these are only valid at the specified frequency and bias conditions


Admittance (y) Parameters

2-porti1

v1

i2

v2y12v2 y22 y21v1

Two-port schematic

y11

Definition = += +

or in matrix format:

=


Impedance (z) Parameters

Two-port schematic

2-porti1

v1

i2

v2z12i2

z22z21i1+ +

- -

z11

Definition

= += +


=


Chain (ABCD) Parameters

Two-port schematic

2-port i1

v1

i2

v2Bi2A-1( )v2

+ - +-

D -1( ) i2Cv2

Definition

= + −= + −


= −

= += +


Measuring Two-Port Parameters

ex. y parameters

y11 =i1v1 v2 =0

• at the same time as port 2 is short-circuited a signal is applied to port 1. The current voltage ratio at port 1 is then:

• A parameter is simply derived when a port voltage is turned to zero, i.e. a port is short-circuited:

2-porti1 i2

v2y11y12v2 y22 y21v1v1


Measuring Two-Port Parameters (cont.)

• Two-port parameters are generally measured by means ofopen (i = 0) or short-circuited (v = 0) ports.

• Open or short-circuited termination is however hard to achieve at high frequencies, especially at the desired location close to the component.

• Open or short-circuited termination may also cause instability and self-oscillation when measurements are performed on active components.

• At higher frequencies there is obviously a need for a model (e.g.S parameters) that doesn’t require open or short-circuited ports.

• y, z and ABCD parameters are still valid for calculations at higher frequencies as well.


Circuit Analysis by Two-Port Parameters

i1i2

é

ëêê

ù

ûúú=

i1a + i1

b

i2a + i2

b

é

ë

êê

ù

û

úú=

y11a + y11

b y12a + y12

b

y21a + y21

b y22a + y22

b

é

ë

êê

ù

û

úú

v1

v2

é

ëêê

ù

ûúú

• parallel connection:use y parameters

2-port ai1

v1

i2

v2y11y12v2 y22 y21v1

2-port b

y12v2 y22 y21v1

• series connection:use z parameters

2-port ai1

av1

i2av2

z1 1 z1 2i2z2 2z2 1i1

+ +

- -

2-port b

bv1

bv2

z1 1 z1 2i2z2 2z2 1i1

+ +

- -

v1

v2

é

ëêê

ù

ûúú=

v1a + v1

b

v2a + v2

b

é

ë

êê

ù

û

úú=

z11a + z11

b z12a + z12

b

z21a + z21

b z22a + z22

b

é

ë

êê

ù

û

úú

i1i2

é

ëêê

ù

ûúú

y11


Circuit Analysis by Two-Port Parameters (cont.)

• cascade connection: use ABCD parameters

v1

i1

é

ëêê

ù

ûúú=

v1a

i1a

é

ë

êê

ù

û

úú= Aa Ba

Ca Da

é

ëêê

ù

ûúú

v2a

-i2a

é

ë

êê

ù

û

úú= Aa Ba

Ca Da

é

ëêê

ù

ûúú

Ab Bb

Cb Db

é

ëêê

ù

ûúú

v2b

-i2b

é

ë

êê

ù

û

úú

2-port a

v1

i2

v2Bi2A-1( )v2

+ - + -

Cv2 D -1( ) i2

2-port b

v1 v2Bi2A-1( )v2

+ - + -

Cv2 D -1( ) i2

i1 i2i1


Parameters for Various Transistor Configurations

• The parameters may easily be converted between different configurations without any loss of information. (Table 8.1 in the textbook)


Power Gain Definitions

G

• How should we define the power gain?

ZS

ZLESPAVS

• PAVS = AVailable power from Source

PIN

• PIN = power delivered to the INput of the two-port

PAVN

• PAVN = AVailable power from Network (the output of the two-port)

PL

• PL = power delivered to the Load


Power Gain Definitions (cont.)

G

ZS

ZLESPAVS PAVN

available gain GA =PAVN

PAVS

PIN PL

operating gain GP =PL

PIN

transducer gain GT =PL

PAVS

Important definitions!


Power Gain from Several Stages

total transducer gain GT tot =PL

PAVS

G1

ZS

ZLES G2 G3PAVS PL

What is the total power gain?

GT tot =PL

PAVS

= POUT1

PAVS

× POUT 2

PIN2

× PL

PIN3

=GT1 ×GP2 ×GP3

Extract the expression by using the gain definitions:

Can GT be calculated in alternative ways? How?


The Gain Expressed by y parameters

GA =gS y21

2

yS + y112 Re y22 -

y12y21

yS + y11

é

ëê

ù

ûú

available gain

GP =gL y21

2

yL + y222 Re y11 -

y12y21

yL + y22

é

ëê

ù

ûú

operating gain

GT =4gSgL y21

2

yS + y11( ) yL + y22( )- y12y212

transducer gain

yiS yL

yS = gS + jbS yL = gL + jbL

yS


Port Admittances for a Two-Port

yin = y11 -y12 × y21

y22 + yL

input admittance

output admittance yout = y22 -y12 × y21

y11 + yS

ySiS yL

yin

®yout

¬

2-porti1

v1

i2

v2y11y12v2 y22 y21v1 y12 connect

output to input


Stability

• If the circuit isn’t able to self-oscillate it is consideredto be stable.

• This is not an obvious quality at RF design because– several feedback paths (parasitic elements)– several reactive circuit elements (parasitic elements)

• Stability analysis based on poles is possible only if the complete circuit is completely known.

• It is not possible to calculate poles and zeros if only two-port parameters are available.There is obviously a need for alternative methods to study stability…


Stability - an Example

Stable when RP > 0 - RP denotes the circuit losses

Unstable when RP < 0 - RP supplies power to the circuit

Poles?

RP LPCP

ZP

ZP =1

sC+1sL

+1R

=sL

s2LC+1+ sLR

=

sC

s2 + s 1RC

+sLR

R > 0 : poles in the left-half planeR < 0 : poles in the right-half plane


Unconditional Stability

yin = y11 -y12 × y21

y22 + yL

yout = y22 -y12 × y21

y11 + yS

Linvill’s stability factor CL =y12 × y21

2 ×g11 ×g22 -Re y12 × y21[ ]

The two-port is unconditionally stable if

Note! The result is only valid at the actual frequency where the stability test is performed

0 < CL < 1

A two-port is defined to be unconditionally stable if no yS or yL results in a negative port admittance


Conditional Stability

• The two-port is stable if the loop resistance rloop > 0– Note! The result is only valid at the actual frequency where

the calculation is done.

rloop = Re zP[ ]+Re zL[ ]xloop = Im zP[ ]+ Im zL[ ]

• If the port impedance still is negative– examine the loop impedance:

• If it’s not unconditionally stable the two-portmay be conditionally stable:

– some yS or yL causes a negative port admittance– avoid these yS and yL if possible

yin = y11 -y12 × y21

y22 + yL

yout = y22 -y12 × y21

y11 + yS

Documents

Lecture 5 Radio Electronics - LTH · – The hybrid-p-model • transistor configurations ... ce =r 0 The hybrid-pmodel for ... (CB) Coupled Transistor