elec 412 - lecture 201 elec 412 rf & microwave engineering fall 2004 lecture 20

ELEC 412 - Lecture 20 1

ELEC 412

RF & Microwave Engineering

Fall 2004

Lecture 20


What Does Stability Mean?• Stability circles determine what load or source

impedances should be avoided for stable or non-oscillatory amplifier behavior

• Because reactive loads are being added to amp the conditions for oscillation must be determined

• So the Output Stability Circle determine the L or load impedance (looking into matching network from output of amp) that may cause oscillation

• Input Stability Circle determine the S or impedance (looking into matching network from input of amp) that may cause oscillation


Criteria for Unconditional Stability

• Unconditional Stability when amplifier remains stable throughout the entire domain of the Smith Chart at the operating bias and frequency. Applies to input and output ports.

• For |S11| < 1 and |S22| < 1, the stability circles reside completely outside the |S| = 1 and |L| = 1 circles.


Unconditional Stability: Rollett Factor

• |Cin| – rin | >1 and |Cout| – rout | >1

• Stability or Rollett factor k: 2 2 2

11 22

12 21

11

2

S Sk

S S

with |S11| < 1 or |S22| < 1

and 11 22 12 21 1S S S S


Stabilization Methods

• Stabilization methods can be used to for operation of BJT or FET found to be unstable at operating bias and frequency

• One method is to add series or shunt conductance to the input or output of the active device in the RF signal path to “move” the source or load impedances out of the unstable regions as defined by the Stability Circles


Stabilization Using Series Resistance or Shunt Conductance


Stabilization Method: Smith Chart


Constant Gain: Unilateral Design (S12= 0)

• Need to obtain desired gain performance

• Basically we can “detune” the amp matching networks for desired gain

• Unilateral power gain GTU implies S12 = 0


Unilateral Power Gain Equations

• Unilateral Power gain 2 2

221 02 2

11 22

1 1

1 1

S LTU S L

S L

G S G G GS S

• Individual blocks are: 2 2

20 212 2

11 22

1 1

1 1

S LS L

S L

G ; G S ; GS S

• GTU (dB) = GS(dB) + G0(dB) +GL(dB)


Unilateral Gain Circles

max max2 211 22

1 1

1 1S LG ; G

S S

• If |S11| < 1 and |S22 |< 1 maximum unilateral power gain GTUmax when S = S11* and L = S22*

• Normalized GS w.r.t. maximum:

2

2112

max 11

11

1

SSS

S S

Gg S

G S


Unilateral Gain Circles

• Results in circles with center and radii:

2

2222

max 22

11

1

LLL

L L

Gg S

G S

• Normalized GL w.r.t. maximums:

2

2 2

1 1

1 1 1 1i i

i iii ii

g g

ii i ii i

g Sg Sd ; r

S g S g

ii = 11 or 22 depending on i = S or L


Gain Circle Observations• Gi max when i = Sii* and dgi = Sii* of radius rgi

= 0• Constant gain circles all have centers on line

connecting the origin to Sii*

• For the special case i = 0 the normalized gain is: gi = 1 - | Sii |2 and dgi = rgi = | Sii |/(1 + | Sii |2)

• This implies that Gi = 1 (0dB) circle always passes through origin of i - plane


Input Matching Network Gain Circles

S is detuned implying the matching network is detuned


Bilateral Amplifier Design (S12 included)

• Complete equations required taking into account S12: Thus S* S11 and L* S22

12 21 1111

22 221 1* L LS

L L

S S SS

S S

12 21 2222

11 111 1* S SL

S S

S S SS

S S


Bilateral Conjugate Match• Matched source reflection coefficient

2

1 1 1

1 1 1

14

2 2

*

MSB B C

C C C

2 2 2

1 11 22 1 22 111*C S S ; B S S

• Matched load reflection coefficient2

2 2 2

2 2 2

14

2 2

*

MLB B C

C C C

2 2 2

2 22 11 2 11 221*C S S ; B S S


Optimum Bilateral Matching

12 2111

221MS

* ML

ML

S SS

S

12 2122

111ML

* MS

MS

S SS

S


Design Procedure for RF BJT Amps• Bias the circuit as specified by data sheet

with available S-Parameters

• Determine S-Parameters at bias conditions and operating frequency

• Calculate stability |k| > 1 and || < 1?

• If unconditionally stable, design for gain

• If |k| 1 and || 1 then draw Stability Circles on Smith Chart by finding rout, Cout, rin, and Cin radii and distances for the circles


Design Procedure for RF BJT Amps

• Determine if L ( S22* for conjugate match) lies in unstable region – do same for S

• If stable, no worries. • If unstable, add small shunt or series

resistance to move effective S22* into stable region – use max outer edge real part of circle as resistance or conductance (do same for input side)

• Can adjust gain by detuning L or S


Design Procedure for RF BJT Amps• To design for specified gain, must be less than GTU

max (max unilateral gain small S12)

• Recall that (know G0 = |S21|2)

GTU [dB] = GS [dB] + G0 [dB] + GL [dB]

• Detune either S or L

• Draw gain circles for GS (or GL) for detuned S (or L) matching network

• Overall gain is reduced when designed for (a) Stability and (b) detuned matching netw0rk


Design Procedure for RF BJT Amps

• Further circles on the Smith Chart include noise circles and constant VSWR circles

• Broadband amps often are feedback amps


RF Shunt-Shunt Feedback Amp Design

1 0 211R Z S 0

2

21

1

m

ZR

R g

Cm

T

Ig

V S21 calculated from desired gain G


Distortion: 1 dB Compression


Distortion: 3rd Order Intermodulation Distortion


Distortion: 3rd Order IMD 2 2 13 dB dBm (2 ) dBmout outIMD P f P f f

0 ,

2dB dBm dB dBm

3f in mdsd IP G P

Spurious Free Dynamic Range

elec 412 - lecture 201 elec 412 rf & microwave engineering fall 2004 lecture 20

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