A filter can separate high and low frequencies. With input of different frequencies, the high-pass filter allows the higher frequencies to produce output voltage across the load; a low-pass filter provides output voltage at lower frequencies.
Pulsating or fluctuating direct current varies in amplitude but does not reverse its direction. Similarly, a pulsating or fluctuating dc voltage varies in amplitude but maintains one polarity, either positive or negative.
Pulsating direct current or voltage consists of a steady dc level, equal to the average value, and an ac component that reverses in polarity with respect to the average level. The dc and ac can be separated by filters.
An RC coupling circuit is a high-pass filter for pulsating direct current. Capacitance CC blocks the steady dc voltage but passes the ac component.
A transformer with an isolated secondary winding also is a high-pass filter. With pulsating direct current in the primary, only the ac component produces output voltage in the secondary.
A bypass capacitor in parallel with R provides a low-pass filter.
Combinations of L, C, and R can be arranged as L, T, or π filters for more selective filtering. All three arrangements can be used for either low-pass or high-pass action. See Figs. 26–9 and 26–11.
In high-pass filters, the capacitance must be in series with the load as a coupling capacitor with shunt R or L across the line.
For low-pass filters, the capacitance is across the line as a bypass capacitor, and R or L then must be in series with the load.
The cutoff frequency fc of a filter is the frequency at which the output voltage is reduced to 70.7% of its maximum value.
For an RC low-pass or high-pass filter, XC = R at the cutoff frequency. Similarly, for an RL lowpass or high-pass filter, XL = Rat the cutoff frequency. To calculate fc for an RC low-pass or high-pass filter, use the formula fc = 1/2πRC. To calculate fc for an RL low-pass or high-pass filter, use the formula fc = R/2πL.
For an RC or RL filter, either lowpass or high-pass, the phase angle 0 between Vin and Vout is approximately 0° 0 = ±90° in the passband. In the stopband, The sign of 0 depends on the type of filter.
RC low-pass filters can be combined with RC high-pass filters when it is desired to either pass or block only a certain band of frequencies. These types of filters are called band-pass and bandstop filters, respectively.
The decibel (dB) unit of measurement is used to compare two power levels. A passive filter has an attenuation of - 3dB at the cutoff frequency.
Semilog and log-log graph paper are typically used to show the frequency response of a filter. On semilog graph paper, the vertical axis uses conventional linear spacing; the horizontal axis uses logarithmically spaced divisions.
The advantage of using semilog or log-log graph paper is that a larger range of values can be shown in one plot without losing resolution in the smaller values.
A band-pass or band-stop filter has two cutoff frequencies. The bandpass filter passes to the load those frequencies in the band between the cutoff frequencies and attenuates all other frequencies higher and lower than the passband. A band-stop filter does the opposite, attenuating the band between the cutoff frequencies, while passing to the load all other frequencies higher and lower than the stopband.
Resonant circuits are generally used for band-pass or band-stop filtering with radio frequencies.
For band-pass filtering, the series resonant LC circuit must be in series with the load, for minimum series opposition; the high impedance of parallel resonance is across the load.
For band-stop filtering, the circuit is reversed, with the parallel resonant LC circuit in series with the load; the series resonant circuit is in shunt across the load.
A wavetrap is an application of the resonant band-stop filter.
