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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
1 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
Transistors at Radio Frequency
® Transistors are more complex at high frequencies due to the effects of
internal 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 independent
measurements to form a physical model to predict S-parameters.
2 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
BF199 VHF Transistor
3 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
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:
(1 + S22)(1 − S11) + S12S21
yi =
∆Z0
−2S12
yr =
∆Z0
−2S21
yf =
∆Z0
(1 + S11)(1 − S22) + S12S21
yo =
∆Z0
where ∆ = (1 + S11)(1 + S22) − S21S12.
6 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
Definition of Y-parameters
® Need these for employ solve.
Ii = yiVeb + yr Vec
Io = yf Veb + yoVec
7 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
Using Solve For Transistors
® Consider the base node
Ib = (yi + yr )Veb − yr Vcb
® Consider the collector node
Ic = (yo + yf )Vec − yf Vbc
® Consider the emitter node
Ie = (yi + yf )Vbe + (yr + yo)Vce
8 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
BF199 S-parameters
® Use Cbe = 100pF (fT = 550M Hz), Cbc = 0.5pF , Ic = 7mA and
hf e = 100.
|S |
11
1
0.5
0 7 8 9
10 10 10
angle S
11
200
100
Degrees
0
−100
−200 7 8 9
10 10 10
frequency (Hz)
9 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
BF199 S-parameters
® Use Cbe = 100pF (fT = 550M Hz), Cbc = 0.5pF , Ic = 7mA and
hf e = 100.
|S |
21
30
20
10
0 7 8 9
10 10 10
angle S
21
200
150
Degrees
100
50
0 7 8 9
10 10 10
frequency (Hz)
10 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
BF199 S-parameters
® Use Cbe = 100pF (fT = 550M Hz), Cbc = 0.5pF , Ic = 7mA and
hf e = 100.
|S |
12
0.06
0.04
0.02
0 7 8 9
10 10 10
angle S
12
150
100
Degrees
50
0 7 8 9
10 10 10
frequency (Hz)
11 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
BF199 S-parameters
® Use Cbe = 100pF (fT = 550M Hz), Cbc = 0.5pF , Ic = 7mA and
hf e = 100.
|S |
22
1
0.5
0 7 8 9
10 10 10
angle S
22
0
−5
Degrees
−10
−15
−20 7 8 9
10 10 10
frequency (Hz)
12 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
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.
13 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
Stability Criteria
® Is the transistor stable in isolation? Linville criterion
|yr yf |
C =
2gigr − real(yr yf )
® Often we need to know if a transistor amplifier is stable.
® If a transistor with given y-parameters is loaded by source and load
admittances YS = GS + jBS and YL = GL + jBL, then the transistor
circuit is unconditionally stable if,
2(gi + GS )(go + GL)
K = > 1
|yr yf | + real(yr yf )
® The Stern Stability Criterion
® A number of useful related formulae.. see the web brick.
14 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
Klapp RF Oscillator
® Model the transistor using S and Y parameters in exactly the same way as
the transistor amplifier.
® In the project the oscillator is a VCO: the MC145170 PLL has to control the
frequency of the oscillator by applying a voltage to a varactor diode or
voltage 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 and
determine the frequency at which the ractance of the input impedance is
zero and the resisitance is negative. WHY?
15 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
Varactor Diode
16 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
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
BF199 local oscillator
1000
Real(Z) at node 1
500
0
−500
−1000
1 2 3 4 5 6 7 8 9 10
7
x 10
1000
Imag(Z) at node 1
500
0
−500
−1000
1 2 3 4 5 6 7 8 9 10
7
x 10
21 ENGN4545/ENGN6545: Radiofrequency Engineering L#13
