Transistors at Radio Frequency ➤ How to describe transistors at radiofrequency.

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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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.
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ENGN4545/ENGN6545: Radiofrequency Engineering L#13
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:
(1 + S22)(1 − S11) + S12S21
yi =
∆Z0
−2S12
yr =
∆Z0
yf =
−2S21
∆Z0
(1 + S11)(1 − S22) + S12S21
yo =
∆Z0
where ∆ = (1 + S11)(1 + S22) − S21S12.
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Definition of Y-parameters
➤ Need these for employ solve.
Ii = yiVeb + yr Vec
Io = yf Veb + yoVec
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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
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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
10
8
9
10
10
angle S
11
Degrees
200
100
0
−100
−200 7
10
9
8
10
frequency (Hz)
ENGN4545/ENGN6545: Radiofrequency Engineering L#13
9
10
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
10
8
9
10
10
angle S
21
Degrees
200
150
100
50
0 7
10
10
8
10
frequency (Hz)
9
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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
10
8
9
10
10
angle S
12
Degrees
150
100
50
0 7
10
11
8
10
frequency (Hz)
9
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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
10
8
9
10
10
angle S
22
Degrees
0
−5
−10
−15
−20 7
10
12
8
10
frequency (Hz)
9
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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.
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Stability Criteria
➤ Is the transistor stable in isolation? Linville criterion
C =
|yr yf |
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.
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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?
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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
BF199 local oscillator
Real(Z) at node 1
1000
500
0
−500
−1000
1
2
3
4
5
6
7
8
9
10
7
x 10
2
3
4
5
6
7
8
9
10
7
x 10
Imag(Z) at node 1
1000
500
0
−500
−1000
1
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