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SIGNAL TO NOISE RATIOBY: ENGR. JO-ANN V. MAGSUMBOL

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SIGNAL-TO-NOISE RATIO- abbrev. as S/N, usually expressed in dB- Ratio of the relative strength of the desired

signal power to the noise power at the same point.

- Expresses in decibels the amount by which a signal level exceeds its corresponding noise

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- 10dB – for barely intelligible speech- 90dB or more – for compact-disc audio

system- Minimum requirement S/N ratio in

corresponding end instruments:

a. Voice = 30dB

b. Video = 45dB

c. Data = 15 dB

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SIGNAL-TO-NOISE POWER RATIO

1. Ideal Case

(S/N)out = (S/N)in

(S/N)In (S/N)out

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SIGNAL-TO-NOISE POWER RATIO

2. Practical Case

(S/N)In (S/N)out

(S/N)out = (Apsin )/(ApN in+Ninternal)

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S (dB) = 10 log PsN PN

S (dB) = 20 log VsN VN

( S + N )N

( S + N + D )N

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NOISE FIGURE- abbrev. as NF or just F- Is a figure of merit, indicating how much a

component, stage, or series of stages degrades the signal-to-noise ratio of a system

- Is a measure of the noise produced by a practical network compared to an ideal network (i.e one that is noiseless)

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- Is equal to the S/N of an ideal system divided by the S/N at the output of the receiver or amplifier under test, both working at the same temperature over the same bandwidth and fed from the same source.

- Degradation of the signal-to-noise ratio by the network

- Occasionally called Noise Factor- Is a measure of the noisiness of the input

stage. It determines the effect that the internal noise, produced by that stage, has on the received signal.

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- Sometimes the term Noise Ratio, reserving the term “Noise figure” for decibel form

(S/N)i (S/N)o

NF = 10 log NFNF(dB)=

NF(dB) = (S/N)i dB – (S/N)o dB

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A. For a noiseless network

(S/N)i = (S/N)o ;

NF = 1

NF(dB) = 0

B. For a network that contributes some noise

(S/N)i > (S/N)o ;

NF > 1

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EXAMPLES1. A radio receiver produces a noise power of

200mW with no signal. The output level increases to 5W when a signal is applied. Calculate (S + N)/N as a power ratio and in decibels.

2. A transistor amplifier has a measured S/N power of 10 at its input and 5 at its output. Calculate the transistors’ noise figure in dB.

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EXAMPLES3. The signal power at the input to an amplifier

is 100µW and the noise power is 1µW. At the output, the signal power is 1W and the noise power is 30mW. What is the amplifier noise figure, as a ratio?

4. The signal at the input of an amplifier has an S/N of 42dB. If the amplifier has a noise figure of 6dB, what is the S/N at the output(in dB)?

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EXAMPLES5. Consider a receiver with an NF of 10dB. Its

output S/N ratio is 50dB. What is its input equivalent S/N ratio?

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EQUIVALENT NOISE TEMPERATURE

- The thermal noise that the device adds to a system

- It is the absolute temperature of a resistor that, connected to the input of a noiseless amplifier of the same gain, would produce the same noise at the output as the device under discussion.

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EQUIVALENT NOISE RESISTANCE

►

►

SN i

SN o

a. Real Noisy Amplifier

SN i

SN oNoiseless

Amplifier

Power Gain ANF = 0dB

Power Gain A

b. Equivalent Noise Resistance and Ideal Amplifier

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ADVANTAGES OF NOISE TEMPERATURE

1. It is additive, like noise power

2. For low noise levels is that it shows a greater variation for any given noise-level change than does the noise figure; changes are easier to grasp in their true perspective.

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Teq = 290(NF-1)

NF = Teq + 1

290

Where:Teq – equivalent temperatureNF – Noise figure

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NOISE FIGURE – NOISE TEMPERATURE CONVERSION

NFdB Teq(K)approx NFdB Teq(K) approx

15 8950 6 86514 7000 5 62713 5500 4 43912 4300 3 28911 3350 2.5 22610 2610 2.0 1709 2015 1.5 1208 1540 1.0 757 1165 0.5 35.4

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EXAMPLES

1. An amplifier has a noise figure of 2dB. What is its equivalent noise temperature?

2. Consider a receiver with an equivalent noise temperature of 290K. What is its NF?

3. A satellite receiving system includes a dish antenna (Teq=35K) connected via coupling network (Teq=40K) to a microwave receiver (Teq=52K).

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EXAMPLES

What is the noise power to the receivers

input over a 1-MHz frequency range. Determine the receivers NF.

4. A receiver has an NF of 10dB. What is its equivalent noise temperature in Kelvin's?

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CASCADED AMPLIFIERS

► ►Stage 1 Stage 2

Gain A1

NF1

Gain A2

NF2

NF1 + (NF2-1) + (NF3 –1) + (NF4-1) + …. A1 A1A2 A1A2A3

NFT =

FRIIS’ FORMULA: