# Band Pass Filters for MHz

I have come across the following site: Passive Band Pass Filter - Electronics Tutorials.

It is a tutorial about band passive filter circuits. The following formular is given with:

$$C=\frac{1}{2 \pi f_c R}$$

$C$ is the capacitor, $R$ the resistor and $f$ the frequency.

So if I want to calculate the needed value for my capacitor I just need to fill in. If $f$ is in the kHz range I get a value for my capacitor with at least $10^{-9}F$. But what if I want to just allow e.g. 400MHz-450MHz, then I get an extremly small value for my capacitor, even with resistors of low resistance. Should the capacitor then just be leaved? Or is this the wrong way to get a band pass filter in the MHz band?

## 2 Answers

I get an extremly small value for my capacitor, even with resistors of low resistance. Should the capacitor then just be leaved?

Of course you don't omit the capacitor. If R is 100 ohms then C = 4pF for 400MHz. A capacitor that small is commonplace at VHF and UHF. But, for a bandpass filter I'd be looking at using inductors, capacitors and resistors to get a sharper rejection of unwanted frequencies. It all depends on exactly what you require of the filter.

This interactive calculator allows an RLC bandpass filter to be simulated like this: -

The value for the capacitor is 27 pF and the inductor is 6 nH.

• Thanks, but if R is 100 ohms i get less than 4pf as frequency has to be filled in as Hz, so 400MHz = 400,000KHz = 400,000,000Hz or? Mar 19, 2015 at 13:35
• @user3852496 If I put your formula in Excel and use R=100 and F=400000000, I get C=3.978e-12 which is approx 4pF. Mar 19, 2015 at 13:50
• up, sry you're right I had interchanged the units. Mar 19, 2015 at 13:55

At first, you should know that the bandpass circuit as shown in the reference is the worst you can ever think. More than that, the formulas given in the tutorial apply only if both corner frequencies of the bandpass are not close to each other (in the example, as shown in the tutorial, it is a factor of 50 between both characteristic frequencies).

For a somewhat better selection (smaller bandwidth) another formula applies; however, in this case, the filter quality factor cannot be above 0.33 (which is very small). At the end of the tutorial, a decoupling buffer is recommended - however, also in this case, the quality factor cannot be larger than Q=0.5.

The best performance can be achieved (a) with a passive RLC combination or (b) with an active filter structure (bandpass in S&K or MFB topology). In the latter case, you need an opamp with a gain-bandwidth producht that is larger than the desired center frequency by a factor of 20...50 (at least).