PHYS225 Lecture 15 Electronic Circuits
Last lecture Difference amplifier Differential input; single output Good CMRR, accurate gain, moderate input impedance Instrumentation amplifier Differential input; single output Excellent performance relative to difference amplifier High CMRR, wider gain choices, high input impedance, lower noise Vast application and documentation Differential output amplifier Differential input and output Good for ADC applications
Frequency Response Graph Gain (in db) Ratio of output against input 20*log (V out /V in ) Always negative value -3dB Point 3dB drop of signal power from highest point on gain Signal power is half of original value Cutoff Frequency (in Hz) Frequency at -3dB Point
Frequency Response Graph Plot of Gain versus Frequency of signal Semi-logarithmic scale Linear Y-axis, logarithmic X-axis Gain (db) (linear scale) 3 db Max Gain (db) Gain is 3 db lower than the max Bandwidth Cutoff Frequency f (khz) (log scale) Gain vs. Frequency
What are Filters? Eliminate unwanted frequencies High-pass or low-pass Favor desired frequencies Band-pass Bandwidth: frequency range filter allows to pass Band-stop Example Let everything through except some frequencies Radio tunes in to particular station
Basic Filter Types Low-Pass Filter Low frequencies pass 3dB Point: -3dB Cutoff Frequency: 1590 Hz Bandwidth: 0-1590 Hz
Basic Filter Types High-Pass Filter High frequencies pass 3dB Point: -3dB Cutoff Frequency: 160 Hz Bandwidth: 160 - Hz
Basic Filter Types Band-Pass Filter Limited frequency range passes 3dB Point: -3dB Cutoff Frequencies: 400 and 600 Hz Bandwidth: 400-600 Hz Resonant Frequency (High Response Point): 500 Hz
Basic Filter Types Band-Pass Filter Limited frequency range passes 3dB Point: -3dB Cutoff Frequencies: 400 and 600 Hz Bandwidth: 400-600 Hz Resonant Frequency (Low Response Point): 500 Hz
Basic Filter Types Band-stop Filter Stops a limited range of frequency
Ideal Filters lowpass highpass bandpass bandstop
Realistic Filters lowpass highpass bandpass bandstop
Bandpass Filter A band-pass filter passes all signals lying within a band between a lower-frequency limit and upper-frequency limit and essentially rejects all other frequencies that are outside this specified band. Actual response Ideal response
The bandwidth (BW) is defined as the difference between the upper critical frequency (f c2 ) and the lower critical frequency (f c1 ). BW f f c 2 c1
The frequency about which the pass band is centered is called the center frequency, f o and defined as the geometric mean of the critical frequencies. f o f f c1 c2
The quality factor (Q) of a band-pass filter is the ratio of the center frequency to the bandwidth. Q fo BW The higher value of Q, the narrower the bandwidth and the better the selectivity for a given value of f o. (Q>10) as a narrow-band or (Q<10) as a wide-band The quality factor (Q) can also be expressed in terms of the damping factor (DF) of the filter as : Q 1 DF
Band-stop Filter Band-stop filter is a filter which its operation is opposite to that of the band-pass filter because the frequencies within the bandwidth are rejected, and the frequencies above f c1 and f c2 are passed. Actual response For the band-stop filter, the bandwidth is a band of frequencies between the 3 db points, just as in the case of the band-pass filter response. Ideal response
Filter Response Characteristics There are 3 characteristics of filter response : Butterworth characteristic Chebyshev characteristic Bessel characteristic. Each characteristic is based on the shape of the response
Butterworth Filter response is characterized by flat amplitude response in the passband. Provides a roll-off rate of -20 db/decade/pole. Filters with the Butterworth response are normally used when all frequencies in the passband must have the same gain.
Chebyshev Filter response is characterized by overshoot or ripples in the passband. Provides a roll-off rate greater than - 20 db/decade/pole. Filters with the Chebyshev response can be implemented with fewer poles and less complex circuitry for a given roll-off rate
Bessel Filter response is characterized by a linear characteristic, meaning that the phase shift increases linearly with frequency. Filters with the Bessel response are used for filtering pulse waveforms without distorting the shape of waveform.
Filter design Filters also produce phase shift (time delays) Changes with characteristic Best choice depends on application