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RC Element as a Frequency-Dependent Voltage Divider

The diagram below shows the previously considered RC element once again in a slightly different configuration. Here it is supplied with an alternating voltage U0 (input voltage to the element) and itself supplies an alternating voltage UC to the capacitor (output voltage to the element). This configuration makes it clear that an RC element acts as a frequency-dependent voltage divider. Whereas the active resistance R is frequency-independent, the capacitive reactance XC is inversely proportional to the frequency f. Consequently, the element's output voltage UC drops as the frequency rises. Whereas an RC element permits low frequencies to pass, it progressively blocks higher frequencies. This type of RC element is accordingly termed a low-pass filter.

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As in the case of the purely ohmic voltage dividers used in DC circuits, the output voltage UC can be calculated as follows. The following equation applies.

FILTER CIRCUITS IN ELECTRONICS !

The ratio between the output and input voltages is

FILTER CIRCUITS IN ELECTRONICS !

Z is the element's apparent resistance (impedance).

If this ratio is plotted graphically for specific values of R and C as a function of the frequency (usually represented on a logarithmic axis), the RC element's amplitude response is obtained, as shown in the example below. At low frequencies, the high capacitive reactance causes practically the entire supply voltage to drop across the capacitor. At very high frequencies, the capacitor's impedance drops to nearly zero, thus causing the output voltage to approach zero too.

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The phase displacement j between the voltages also depends on the frequency in accordance with the following equation:

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The negative sign here indicates that the output voltage lags behind the input voltage. Displayed graphically, this relationship is termed the RC element's phase response. At low frequencies, the two voltages are nearly in phase whereas at high frequencies, the phase shift approaches -90°.

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The RC element's amplitude and phase responses together are termed its frequency response.

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