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18 bit ADC thermal noise

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A simplified model of ADC noise refers the noise to a noisy input source resistance Rn while assuming the rest of the signal path to be noiseless. Attached Figure represents a particular 18-bit ADC that has a 10V input voltage range. The ADC has a bandwidth of 1 MHz. Calculate the maximum value of Rn if the resolution of the ADC is not to be adversely affected by thermal noise. Assume the ADC operates at 25 degree C. [N.b. The voltage resolution of an ADC is equal to its overall voltage measurement
range divided by the number of discrete values possible on its output.] Please see the attachment for a schematic.

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To find Rn = ?

Given:
No. of bits N = 18
Voltage range V = 10
temperature T = 25+273 = 298 K
Band width f = 1 MHz = 10^6 Hz

ADC voltage resolution, Vr ...

Solution Summary

This problem estimates maximum resistance, to overcome thermal noise threshold so that ADC signal is resolved properly.

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Multiple electrical signal, level, noise calcualtions

1. FIGURE 1 shows the block diagram of a superhetrodyne radio receiver. In a test a 20 V signal was fed from the aerial into the first stage of the receiver, a radio frequency amplifier. This signal is then passed through several stages of the receiver to eventually appear at the input to the AM detector. For the AM detector to work satisfactory it requires a minimum signal level of -3dB(mW). Calculate the required minimum gain of the fifth intermediate amplifier given the data in TABLE 1.

Stage Gain
RF amplifier +10 dB
Mixer -7 dB
BPF -1 dB
IF1 +15 dB
IF2 +15 dB
IF3 +20 dB
IF4 +10 dB

TABLE 1

20 V
(75 )

FIG. 1

2. As a rule of thumb, the perceived noise from a source falls by 6 dBA with every doubling of the distance from the source.

If a 1 MW wind turbine (FIGURE 2) produces 103 dBA of noise within one metre of its base, estimate the distance from the turbine at which the noise can be reckoned to have fallen below the background noise level of 40 dBA.

Background level

Distance

FIG. 2

3. A simplified model of ADC noise refers the noise to a noisy input source resistance Rn while assuming the rest of the signal path to be noiseless.
FIGURE 3 represents a particular 18-bit ADC that has a 10 V input
voltage range. The ADC has a bandwidth of 1 MHz.

Calculate the maximum value of Rn if the resolution of the ADC is not to be adversely affected by thermal noise. Assume the ADC operates at 25°C.

[N.b. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete values possible on its output.]

Analogue input

Rn

1

Digital output 18 lines
18

FIG. 3

4. The specification for a 4-way TV antenna amplifier [FIGURE 4] is given
in TABLE 2, below.

TABLE 2

FIG. 4

(a) Determine the voltage required on the input of the amplifier to give the maximum output of 85 dBV.

(b) If the signal level from the aerial is 5 dBmV and the input noise level is 20 dBV, calculate the signal-to-noise ratio on the output of the amplifier.

5. A voltage amplifier ideally should have the input-output relationship of
vo = 100vi but in practice the relationship is vo = vi(98 + 2vi).

Calculate the %age second harmonic distortion present in the amplifier's output for a sinusoidal input of 10 mV r.m.s.

Note: Question 6 from the attachment is not addressed, as data is missing from previous questions.

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