# Question: a Prove that the expression for the PSD of thermal

(a) Prove that the expression for the PSD of thermal noise in a resistor converges to the constant as No / 2 = ktk / 2 as f→0.

(b) Assuming a temperature of 298ok, find the range of frequencies over which thermal noise has a PSD which is within 99% of its value at f = 0.

(c) Suppose we had a very sensitive piece of equipment which was able to accurately measure the thermal noise across a resistive element. Furthermore, suppose our equipment could respond to a range of frequencies which spanned 50 MHz. Find the power (in watts) and the RMS voltage (in volts) that we would measure across a 75 Ω resistor. Assume the equipment had load impedance matched to the resistor.

(b) Assuming a temperature of 298ok, find the range of frequencies over which thermal noise has a PSD which is within 99% of its value at f = 0.

(c) Suppose we had a very sensitive piece of equipment which was able to accurately measure the thermal noise across a resistive element. Furthermore, suppose our equipment could respond to a range of frequencies which spanned 50 MHz. Find the power (in watts) and the RMS voltage (in volts) that we would measure across a 75 Ω resistor. Assume the equipment had load impedance matched to the resistor.

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