MAS.962 Problem Set 2

Second assignment for course MAS.962: Techniques for Design and Fabrication covers three variations of Resistor-Capacitor (RC) circuits:

• Envelope detector (aka Peak detector, pulse stretcher, or half-wave rectifier)
• Low-pass filter
• High-pass filter

Envelope Detector

What it does

• Combination of half/full-wave rectifier and a high-pass filter:
• Chops the bottom half of a high-frequency AC signal and smooths it out, riding along the peaks. See Wikipedia

How it works

• The capacitor in the circuit stores up charge on the rising edge, and releases it slowly through the resistor when the signal falls.
• The diode in series ensures current does not flow backward to the input to the circuit.

How to build it

Use a function generator to provide varying input AC voltage. Measure V-out with an oscilloscope.

Varying input voltage frequency

5Vp-p sinusoid, change frequency from 1Hz >> 1KHz >> 100 KHz:

Time to decay

Time to decay (sec) = 4 * R (ohm) * C (farad)

• 5Vp-p square wave, measure how long it takes for the V-out to become 0V.
• T = 4 * 10^4 * 10^-7 = 4^-3 sec = 4ms
• 10Vp-p square wave: Time to decay is the same as 5Vp-p.
• Increase R from 10Kohm to 100Kohm: Time to decay is now 40ms.

• Small R: More precision
• Large R: Smoother V-out curve

Low-Pass Filter

• Coupling capacitors act to pass a range of AC signals from one circuit to another.
• Capacitors are basically frequency-dependent resistors.
• High frequency: Low impedance (easy to flow)
• Low frequency: High impedance (difficult to flow)
• High-frequency signal gets shorted out because of the low impedance in parallel with the load resistance, dropping most of the voltage across series resistor.
• RC low-pass filter passes low-frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency.

Cutoff Frequency

• Frequency characterizing a boundary between a passband and a stopband
• -3dB frequency, 1/2 power point
• The frequency either above which or below which the power output of a circuit, such as a line, amplifier, or electronic filter is the power of the passband.
• Because power is proportional to the square of voltage, the voltage signal is of the passband voltage at the corner frequency.
• Hence, the corner frequency is also known as the −3 dB point because is approximately −3 decibels.
• The resistance times the capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency, at which the output power is half the input (−3 dB):
  
• Where f is in hertz, τ is in seconds, R is in ohms, and C is in farads.

How to build it

R=10K, C = 0.1uF; apply sinusoidal AC input of 10Vp-p; measure the amplitude of V-out as you increase V-in frequency.

Cutoff frequency: Approx 150-200Hz (160Hz according to formula)

High-Pass Filter

• Offers easy passage of a high-frequency signal and difficult passage to a low-frequency signal.
• The capacitor’s impedance increases with decreasing frequency.
• This high impedance in series tends to block low-frequency signals from getting to load.

How to build it

R=10K, C = 0.1uF; apply sinusoidal AC input of 10Vp-p; measure the amplitude of V-out as you increase V-in frequency.

Cutoff frequency: Approx 150-200Hz (160Hz according to formula)

A picture of the low-pass filter (missing LM 7805 power regulator)