Transistors at Radio Frequency

➤ How to describe transistors at radiofrequency.

➤ Equivalent circuits and S-parameters

➤ Y-parameters and SOLVE

➤ Stability of transistor amplifiers (brief)

➤ The Klapp RF Oscillator

➤ SOLVE Example: The Klapp Oscillator

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Transistors at Radio Frequency

➤ Transistors are more complex at high frequencies due to the effects ofinternal parasitic inductance and capacitance.

➤ Always try first to seek S-parameters from manufacturers.

➤ Or use a simulation package that has them in its database.

➤ Failing all this.. do a model. Here’s how.

➤ We try to glean enough information from datasheets and independentmeasurements to form a physical model to predict S-parameters.

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BF199 VHF Transistor

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Radio Frequency Transistor circuit model

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BF199 Datasheet

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Networks: Y-parameters vs S-parameters

➤ Y-parameters and S-parameters are related:

yi =(1 + S22)(1 − S11) + S12S21

∆Z0

yr =−2S12

∆Z0

yf =−2S21

∆Z0

yo =(1 + S11)(1 − S22) + S12S21

∆Z0

where ∆ = (1 + S11)(1 + S22) − S21S12.

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Definition of Y-parameters

➤ Need these for employ solve.

Ii = yiVeb + yrVec

Io = yfVeb + yoVec

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Using Solve For Transistors

➤ Consider the base node

Ib = (yi + yr)Veb − yrVcb

➤ Consider the collector node

Ic = (yo + yf)Vec − yfVbc

➤ Consider the emitter node

Ie = (yi + yf)Vbe + (yr + yo)Vce

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BF199 S-parameters

➤ Use Cbe = 100pF (fT = 550MHz), Cbc = 0.5pF , Ic = 7mA andhfe = 100.

107

108

109

0

0.5

1

|S11

|

107

108

109

−200

−100

0

100

200

frequency (Hz)

Deg

rees

angle S11

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BF199 S-parameters

➤ Use Cbe = 100pF (fT = 550MHz), Cbc = 0.5pF , Ic = 7mA andhfe = 100.

107

108

109

0

10

20

30

|S21

|

107

108

109

0

50

100

150

200

frequency (Hz)

Deg

rees

angle S21

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BF199 S-parameters

➤ Use Cbe = 100pF (fT = 550MHz), Cbc = 0.5pF , Ic = 7mA andhfe = 100.

107

108

109

0

0.02

0.04

0.06

|S12

|

107

108

109

0

50

100

150

frequency (Hz)

Deg

rees

angle S12

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BF199 S-parameters

➤ Use Cbe = 100pF (fT = 550MHz), Cbc = 0.5pF , Ic = 7mA andhfe = 100.

107

108

109

0

0.5

1

|S22

|

107

108

109

−20

−15

−10

−5

0

frequency (Hz)

Deg

rees

angle S22

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Example: A BF199 Common Emitter Amplifier

➤ Use the large signal equivalent (left) to set the bias point.➤ Use the small signal equivalent (right) to set up SOLVE.

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Stability Criteria

➤ Is the transistor stable in isolation? Linville criterion

C =|yryf |

2gigr − real(yryf)

➤ Often we need to know if a transistor amplifier is stable.

➤ If a transistor with given y-parameters is loaded by source and loadadmittances YS = GS + jBS and YL = GL + jBL, then the transistorcircuit is unconditionally stable if,

K =2(gi + GS)(go + GL)

|yryf | + real(yryf)> 1

➤ The Stern Stability Criterion

➤ A number of useful related formulae.. see the web brick.

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Klapp RF Oscillator

➤ Model the transistor using S and Y parameters in exactly the same way asthe transistor amplifier.

➤ In the project the oscillator is a VCO: the MC145170 PLL has to control thefrequency of the oscillator by applying a voltage to a varactor diode orvoltage variable capacitor (VVC) .

➤ We need to prove that the oscillator will oscillator and at what frequency.

➤ In SOLVE we inject a current into the tank circuit of the oscillator anddetermine the frequency at which the ractance of the input impedance iszero and the resisitance is negative . WHY?

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Varactor Diode

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Klapp RF Oscillator

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Using SOLVE: Compute S-parameters and Y-parameters

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Using SOLVE: Set circuit values

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Using SOLVE: Set SOLVE admittances

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KLAPP oscillator input impedance

1 2 3 4 5 6 7 8 9 10

x 107

−1000

−500

0

500

1000

Rea

l(Z)

at n

ode

1

BF199 local oscillator

1 2 3 4 5 6 7 8 9 10

x 107

−1000

−500

0

500

1000

Imag

(Z)

at n

ode

1

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