Digital Control Systems Waseem Gulsher BS (Evening) 18 Dec, 17 Signal Conditioning Lecture - 13 Digital Control Systems Waseem Gulsher

Filters

High Pass Filter The high pass filter is designed to pass all frequencies that are above a lower cutoff frequency, f1. All frequencies normally applied to this circuit that are above f1 are passed by the circuit.

High Pass Filter

High Pass Filter The high pass filter differs from the low pass filter in two respects: The resistors and capacitors have swapped positions. The multi-pole circuits are designed to fulfill the following conditions:

High Pass Filter

High Pass Filter Since the capacitors are in series with the amplifier input, they limit the low-frequency operation of the circuit. The value of f1 for each circuit is found using the same equation that were used to find f2 for the equivalent low pass filter.

High Pass Filter As frequency decreases, the reactance of a series capacitor increases. This causes a larger portion of the input signal to be dropped across the capacitor. When the operating frequency has dropped to f1, the series capacitors causes the gain of the amplifier to drop by 3dB.

Filter Gain Requirements As frequency decreases, the reactance of a series capacitor increases. This causes a larger portion of the input signal to be dropped across the capacitor. When the operating frequency has dropped to f1, the series capacitors causes the gain of the amplifier to drop by 3dB.

One-Pole High-Pass Filter

Two-Pole High-Pass Filter

Three-Pole High-Pass Filter

Band Pass Filter The band pass filter is designed to pass only the frequencies that fall between the values of f1 and f2.

Two-Stage Band-Pass Filter It is common for a band-pass filter to be constructed by cascading a high-pass filter and a low-pass filter.

Two-Stage Band-Pass Filter The first stage of the amplifier will pass all frequencies that are below its value of f2. All the frequencies passed by the first stage are coupled to the second stage, which passes all frequencies above its value of f1. The result of this circuit is shown on next slide.

Two-Stage Band-Pass Filter

Two-Stage Band-Pass Filter Note that the only frequencies that pass through the amplifier are those that fall within the pass band of both amplifiers. The frequency analysis of the circuit shown earlier is relatively simple. The values of f1 and f2 are as calculated for low-pass filter and high-pass filter.

Two-Stage Band-Pass Filter Once the values of f1 and f2 are known, the circuit values of bandwidth, center frequency and Q are found as follow:

Example Perform the complete analysis of the following amplifier.

Solution The value of f2 is determined by the first stage of the circuit (the low-pass filter) as follow

Solution The value of f1 is determined by the second stage of the circuit (the high-pass filter) as follow

Solution Thus, the circuit would pass all frequencies between 750Hz and 1.13kHz. All other frequencies would effectively be blocked by the band-pass filter.

Solution Now the values of f1 and f2 are known, we can solve for the amplifier bandwidth as follow

Solution The center frequency is found as

Solution Finally, the value of Q is found as

Assignment # 3 Design a Band-Stop filter which should stop the frequencies between 500 KHz to 900KHz. Also find the Q of said filter. Date of Submission : 22 Dec, 17 Compensatory Class : 22 Dec, 17 at 04:00pm.

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