Over specifying a capacitor too much will add extra cost size and weight under specifying it will lead to poor performance. Therefore the size of the input bulk capacitor is determined by the size of the output current transient and the allowable input voltage deviation.

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This capacitance appears in parallel with cout.

Output capacitor size. The dc output of a lightly loaded 24v transformer is roughly 24 12 1414 40v that is generally too high for most 3 terminal regulators. Because these capacitors have a dc value they are actually storing a lot of energy that never gets used. With 32 ohm grados and a 470uf output cap there will be some phase distortion as high as oh 80hz or so.
The circuit driven by the supply can and often will contribute additional capacitance for example the sum of the power rail bypass capacitors in a connected circuit. Regarding the input capacitor virtually any capacitance will work for flea power microamp load. Coupling capacitor calculator that calculates optimal coupling cap values based on the input impedence of load and the desired low frequency response you desire the inner details of the music seem better revealed sometimes for the first time.
Capacitor smoothing circuits calculations. Typical capacitor ratings range from 470 pf to 47 nf at voltage ratings as high as 2000 vdc. To smooth the output of the rectifier a reservoir capacitor is used placed across the output of the reciter and in parallel with the load.
Why the capacitor in your power supply filter is too big january 21 2016 by david williams the job of the capacitor in the output filter of a dc power supply is to maintain a constant dc value by removing as much power ripple as possible. Its size is purely a function of the current step size and the esr. If the output cap is too small relative to the impedance of your headphones there will be significant smearing of bass frequencies.
For high power semiconductors such as igbts the values can be as high as 22 uf with voltages in the range of 1200 vdc. Output capacitor applications may not be an issue as the power supply feedback is controlling the current and thus tantalum capacitors can be used here at up to 80 of the capacitorsi rated voltage 20 derating minimum 1. The amplitude of the input voltage deviation during a transient is directly proportional to the load current.

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