# Communications Electronics Exercise 4: Noise Figure and Matching

```Institut für Integrierte Systeme
Integrated Systems Laboratory
Communications Electronics
Exercise 4: Noise Figure and Matching
Xu Han Benjamin Sporrer
Hand out: 14.03.2016
Hand in: 04.04.2016
Problem 1
NF1=3 dB
NF2=7 dB
NF3=15 dB
G1 = 7 dB
G2 = 10 dB
G3 = 10 dB
The overall noise figure of a cascade of several amplifiers can be computed as follows: If the noise
figure is Fi and the gain is Gi for amplifier i, the total noise figure is:
FTOTAL = F1 +
F2 − 1 F3 − 1
F4 − 1
+
+
+ ...
G1
G1 G2 G1 G2 G3
(a) Verify the formula given above for two cascaded amplifiers.
(b) Calculate the total noise figure for the three cascaded amplifiers in Figure 1.
(c) What happens, if one increases the gain of the first amplifier?
Problem 2
(a) Calculate the noise figure of the circuit in Figure 2. Assume that the amplifier is noiseless. (Only
RS and RL contribte to the total noise).
Amplifier
RS
vS
vin
gmvin
Zin
ro
vout
RL
Noiseless
Figure 2: Ideal amplifier.
(b) Re-calculate the noise figure, if the input impedance Zin is matched to RS and the amplifier is
noisy and with an output noise current of:
8
i2out = kT gm ∆ f
3
(c) Determine the output load that allows maximum Power transfer to the output. Does this output
load also minimize the noise figure in this circuit? Calculate.
Problem 3
Figure 3: Transistor configuration.
(a) Draw the small-signal equivalent circuit of the common-gate stage.
(b) Calculate the input impedance Zin = VIinin for a common-gate amplifer in Figure 3.
(c) Calculate Zin , if
ro RL
gm ro 1
(1)
(2)
and use this result for the following questions.
(d) Under which condition for RS and gm can we use the L-section network formed by inductance LS
and capacitance CS to match the source to the input of the amplifier?
2
(e) Given RS = 50 Ω, gm = 7 mA/V and Cgs = 80 fF, please calculate the values of LS and CS , so that
the input is matched at frequency f = 900 MHz.
(f) For the following tasks assume ro → ∞. Assume that CS and LS are chosen to match the source to
the input of the amplifier. (This generates a very simple transfer function from v2RS to v2in,RS !) Do
not use numerical values from task e). Calculate the output reffered noise of the noise generated
by the source resistance and the load resistance. The noise generated by the amplifier is a current
noise from source to drain with
8
i2out = kT gm ∆ f
(3)
3
Calculate also its influence to the output noise.
(g) Calculate the Noise figure of this circuit. Compare the result with the noise figure of the amplifier
in Problem 2.
3
```