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AE_Tutorial 10_Noise

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: This gives problems on Noise Chapter AE-LECTURE9

AE_TUTORIAL NO 10_Problems on NOISE PARAMETRS.

Problem (1) Calculate the available power per Hz of BW for a resistance at room temperature (T=290 K).Express in decibels with reference to 1mW(dBm) And with reference to 1 W(dBW).

Solution: Available power per Hz =kT (W/Hz)

Power in W/Hz=kT=4 x 10-21 W/Hz

Power in dBm=10 log(4 x 10-21/1 x 10-3)= -174dBm

Power in dBW= 10 log(4 x 10-21/1)= -204dBW

PROBLEM(2) Given one port network:

Figure 1
Figure 1 (Picture 1.png)

Determine <v n 2 > at AA’ in BW=100kHz. Also determine the rms voltage at AA’.

SOLUTION: Req at AA’=R3||(R1+R2)

= 1K||(1K+1K)

= 1K||(2K)

= 1 x 2/ 1+2 =2/3 K

Therefore <vn2>|AA’= (4kTB)Req|AA’=(4 x k x 290 x 100 x 103) x (2/3) x 103

=1 x 10-12(V)2

rms noise voltage=

Figure 2
Figure 2 (graphics1.png)

PROBLEM(3) In TV receiver the antenna is often mounted on a tall mast and long lossy cable is used to connect the antenna to the receiver. To overcome the effect of lossy cable, a pre amplifier is mounted on the antenna as shown in the figure.

(a)Find the overall noise figure.

(b)Find the overall noise figure if pre-amplifier is omitted and gain of front end is increased by 20dB.Normally the NOISE FIGURE of the front end of the receiver is 16dB.

Figure 3
Figure 3 (Picture 2.png)

Note: The first stage is the pre-amplifier kept at the top of the mast which carries the antenna. This pre-amplifier is supposed to compensate for the loss occurring while carrying the signal from the antenna to the front end of the receiver.

The second block represents the lossy cable.

The third block is the front end of the receiver which has a noise figure of 16dB.

Solution of Problem(3):

Figure 4
Figure 4 (Picture 3.png)

The noise figure of 2 stages is given by the formula:

Figure 5
Figure 5 (graphics2.png)

Generalizing this result we get

Figure 6
Figure 6 (graphics3.png)

Therefore the overall Noise figure is largely determined by the Noise Figure of the FIRST stage and the gain of the 1st stage. F1 should be very low and the gain

Figure 7
Figure 7 (graphics4.png)
should be very high.

Part(a)

Figure 8
Figure 8 (graphics5.png)

Figure 9
Figure 9 (graphics6.png)

Figure 10
Figure 10 (graphics7.png)

Figure 11
Figure 11 (graphics8.png)
Figure 12
Figure 12 (graphics9.png)
Figure 13
Figure 13 (graphics10.png)

When all three stages are considered:

Figure 14
Figure 14 (graphics11.png)
Figure 15
Figure 15 (graphics12.png)
Figure 16
Figure 16 (graphics13.png)
Figure 17
Figure 17 (graphics14.png)

Part(b) Without the pre-amplifier

Figure 18
Figure 18 (graphics15.png)

In part(b), we have a very bad overall noise figure resulting into a very poor reception of the TV station tuned to.

To overcome this problem we always mount a pre-amplifier on the tall mast which carries the antenna.

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