# How does a filtering capacitor work without a resistor?

Consider the circuit below:

A google search said that the capacitors here are used to filter noise/ripples from the incoming and outgoing signals. How are the capacitors able to do this without a resistor in series? I was told that RC circuits make filters, not capacitors alone. Is it relying on the internal resistance of the battery, or is it because the capacitors themselves have some internal resistance? How would you quantify this, for example, to figure out the cutoff frequency?

• Epix - Hi, When a post copies or adapts material (e.g. text, image, photo etc.) from elsewhere, that content must be correctly referenced. For online content, the source webpage / PDF / video etc. should be named & linked as a minimum (see the rule about references for offline books / articles). Therefore please edit your question to add the appropriate source reference (e.g. source name & link) for that schematic, and remember to include references in future. (Please review the tour & help center as rules here differ from typical forums). TY Commented Jan 23 at 17:39
• Ignoring all the excellent points in the answers, the capacitors are not alone, they have a component in between them. That component drops voltage and gets hot when current flows, so there is definitely a resistance in series with that circuit. If there was no resistance, you wouldn't have heat! Commented Jan 24 at 3:22

The battery is very stable but has some internal resistance. The wires also are not superconductors but they have resistance, and what's even worse, wires have inductance.

The regulator itself cannot respond to varying loads infinitely fast in no time, so it needs capacitance for control loop stabiity.

So any load that is far away and consuming pulsed current, will be a difficult load, for example a basic 8 MHz microcontroller might be on average a 10mA DC load, but im reality it is taking pulses of curret at 8 MHz, and on each clock cycle, it might take 100mA for 10% of the time and 0mA for 90% of the time.

The capacitors here are used to lower the impedance that is a result of the battery internal resistance and the regulator output resistance.

If there is a fast change in load current the output capacitor supplies or soaks up current for a short time while the regulator catches up to the changes. On many regulators (not this one, however) it and the internal resistance of the capacitor are also part of the frequency "compensation" and the cap is required for stability.

The input capacitor supplies current when there are brief demand pulses and can enhance stability. As the battery gets used up the internal resistance increases and the capacitor becomes more important. It's not uncommon to use something like a 100uF/16V electrolytic capacitor rather than the minimum shown in the datasheet.

If you just connect a 7805 with no capacitors at all and a benign load like an LED with series resistor it will work fine, for this kind of regulator. The price you pay for this kind of nice behavior is a high dropout voltage. Many more modern regulators (the 7805 design is more than 50 years old) are far more persnickety about the output capacitor in particular.

Strictly speaking, these are technically bypass capacitors in you schematic. They inherently have a filtering ability by sinking and sourcing current very rapidly to stiffen the lines and suppress transient voltage events. The impendence of the line as an effect on the filtering capability - if the transients come in with no impendence have infinite current sourcing ability, The bypass capacitor will theoretically not help. The "cutoff frequency" in the classical filter sense is dependent on the source impedance, and the capacitor properties (capacitance, ESR, ESL). Adding additional series resistance before the regulator will certainly help with filtering AC components (transients, surges, ripple, emi) at the expense of lost power and a reduction of voltage at the regulator input.

Real capacitors do have some internal resistance and inductance (referred to as ESR and ESL i.e. equivalent series resistance/inductance). Ideal capacitors do not have any resistance or inductance at all and dissipate no power, however, this is impossible with our technology.

The capacitors are repeatedly charged and discharged to minimise voltage ripple and noise (alkaline batteries shouldn't have much ripple in the first place). Usually these capacitors are also used to maintain stability in the linear regulator and prevent output oscillation.

To answer your second question, cut-off frequency is not incredibly important in a simple constant-voltage circuit. Generic aluminium electrolytics can be used as long as their ratings are not exceeded.