# Is a capacitor a high-pass filter or a band-pass filter?

This has been bugging me for a while now... Does a single capacitor, on its own, behave as a high-pass filter or a band-pass filter?

In a crystal radio set, you use a single capacitor as the tuning element, to select which radio frequency the radio will receive. This strongly implies that a capacitor is a band-pass filter.

But reading Wikipedia, it is suggested that a capacitor is actually a 1-pole high-pass filter.

Well, obviously it can't be both. So which is it?

(Bonus points for anybody who can point to an actual frequency response curve.)

• I think in crystal radio sets you tune the capacitor of an LC tank, the capacitor is not the only element. – Samuel Jan 21 '15 at 20:26
• It'd be a low pass if you coupled your signal to ground with the capacitor; it'd be a high pass if the capacitor was in series with the signal. So I guess with a combination of the two I'd imagine you'd be able to make a band-pass filter. – Nick Williams Jan 21 '15 at 20:30
• An ideal capacitor with one lead as the input and the other as the output is a high pass filter since its impedance is $Z_C = 1/(j\omega C)$. At $\omega = 0$ the impedance is $\infty$ (i.e. open circuit = gain of 0). As $\omega \to \infty$ the impedance goes to 0 (i.e. short circuit = gain of 1). But real capacitors do not have this ideal frequency response because of parasitics. – Null Jan 21 '15 at 20:33
• On its own a capacitor does nothing. As part of a circuit (i.e., with other components) it can be part of a low-pass filter, a high-pass filter, a notch filter, a bandpass filter, or whatever, depending on the rest of the circuit. – Pete Becker Jan 21 '15 at 20:49
• While relevant only to substantially different questions which might share your title, the inductance if a practical capacitor gives it a self resonant frequency. – Chris Stratton Jan 22 '15 at 0:27

## 2 Answers

A capacitor by itself is not a filter at all, neither high pass, low pass, nor anything else.

A capacitor can be used as part of a high pass, low pass, or band pass filter, depending on how it's connected to other parts. For example, a capacitor with a resistor can be a high pass filter:

or a low pass filter:

Together with a inductor and some additional impedance (represented by the resistor), it can be a band pass filter:

Or a band rejection filter:

A crystal radio works like the left band pass filter. C1 and L1 form a resonant tank that has high impedance at the resonant frequency and low impedance at other frequencies. Even that by itelf is not a filter, since just a changing impedance isn't a filter. It is the changing impedance working against some other impedance that forms a voltage divider that then makes a filter. In the example above, R1 is that other impedance. In a crystal radio, it is the impedance of the signal coupled to L1 magnetically by the antenna coil. In that case the antenna coil is the primary of a transformer, and L1 is the secondary, which resonates at a particular frequency depending on the value C1 is tuned to.

## Added about crystal radio:

I see from the comments that there is some confusion about how the capacitor in a crystal radio works and how such a radio is tuned. There are different ways a crystal radio can be made, but I'll stick to the very common configuration you can find all over the web, and that is implemented by most crystal radio kits:

The inductor is a single coil, ususally magnet wire wound round something like a carboard toilet paper roll. The coil is essentially a transformer. The transformer primary is the left section between the antenna and the tap. Since the tap is grounded, there is no direct flow of current between the two sections of the coil. Voltage is induced in the right part of the coil by transformer action. The only way for the signal to get from the left part of the coil (the transformer primary) to the right part (the transformer secondary), is by the magnetic coupling between the two parts of the coil.

The transformer creates a higher voltage at its right end, although at a higher impedance. Typical antennas have impedance in the 50-300 Ω range, whereas the crystal radio is intended to drive old style headphones that have a few kΩ impedance. The higher voltage at a higher impedance is a better match to the headphones, and allows the very limited power from the antenna to be used more efficiently.

The inductance of the coil together with the capacitance form a high Q tank circuit. The radio picks up a station when the capacitor is adjusted so that the tank resonates at the station's carrier frequency. Due to the finite impedance of the antenna driving the tank as seen thru the transformer, and the impedance of the headphones loading the output, the capacitor and the coil together form a narrow band pass filter.

• I clicked on this as the answer, but I wanted to add the following link, as something that the asker might want to look at to help understand passive analog circuits: falstad.com/circuit – Jotorious Jan 21 '15 at 21:47
• In summary, then, it is the combination of a capacitor and an inductor that makes it band-pass rather than just high-pass. This answers my literal question - yet at the same time, it seems that there is something drastically wrong with my understanding of this stuff. I will try to pinpoint where I'm going wrong, and ask a separate question... – MathematicalOrchid Jan 21 '15 at 21:48
• In the example you gave, there's little or no mutual inductive coupling between the [long-wire] antenna and the tank coil, so any transformer action between the antenna and the tank coil will be trivial. In reality, depending on the length of the antenna and the wavelength of the RF it intercepts, it'll look like a voltage source series-connected to the tank through an impedance which is either resistive, capacitive, or inductive. – EM Fields Jan 22 '15 at 10:25
• @EMFi: I rolled back your edit for reasons we discussed before. I did then fix the typo in "resistor", but "band rejection filter" makes more sense than "band reject filter". As for the crystal radio, The typical version has a coil wrapped around a paper tube with a tap near one end. The antenna is connected to the end near the tap, and the tap to ground. The resonant coil is from the tap to the other end. The only way for RF to get to the resonant coil is by transformer coupling between the two parts of the coil. – Olin Lathrop Jan 22 '15 at 14:55
• @Doombot: I deliberately stayed away from such issues. The OP has enough confusion just understanding how ideal capacitors work that I felt this isn't the time to introduce the non-ideal characteristics of real components. I'm agreeing with you that these effects are real, but that they are too advanced a topic for this question. – Olin Lathrop Jan 22 '15 at 17:20

A capacitor alone is not usually a filter at all.

It can form either a high-pass or low-pass filter, in conjunction with a resistor, or it can form either of those or a bandpass filter, in conjunction with an inductor.

In the crystal set, if your schematic you are looking at is old enough, there may be no inductor visible, and no good explanation why the capacitor works as a tuning element.

Here, the missing fact is that the antenna itself was acting as the inductor, and the explanations may not make that clear because it may not have been well understood by the writers before sometime around the mid 1920s.