# Lumped Element Filter Calculator

Click here to go to the download area and try out the calculator. Now there's two, check out Vlad's calculator it probably is better than the original Microwaves101 calculator.

This is the answer to many of your problems... your mother-in-law recently asked you "when are you going to design a lumped-element filter for my television antenna so I can reject all that noise from the Henderson's amateur radio station?" Or your wife says "stop picking out wallpaper for the baby's room, you know I need a new lumped-element filter for your niece's confirmation present!" The list goes on and on and on...

Some quirks

Recommended design procedure

Design example 1

Determining filter order

Tee or pi network?

Resizing components for available values

Changing the system impedance

In our recently revised filter spreadsheet (version 2B updated January 10, 2005) we've added plot capabilities inside the Excel spreadsheet. This is VERY COOL, you can design a filter in REAL TIME now, instead of exporting the capacitor and inductor values to an ADS file!

A Chebyshev filter is an equal-ripple filter, and it has an exact mathematical solution (the arithmetic is buried somewhere in the download). The order of the filter (N=3, N=4, etc.) is determined by how many lumped elements (capacitors and inductors) the filter has. In the case of bandpass filters, the capacitors and inductors are paired into resonators; an N=5 filter will have five capacitors and five inductors. Also, for a bandpass filter, the order equal to how many dips there are in the frequency response.

The steepness of the skirts is a dependent variable. If you want steeper skirts (more rejection), allow more ripple in the pass-band, or go to a higher order.

### Quirks

Here are some quirks in the spreadsheet that we still have to work out:

We've recently fixed some labeling and added figures in the spreadsheet to clarify which element is which. It's much better, but we noticed some bugs. The N=4 filter calculator has some major problems, so we have deleted it from this release. The N=3 and N=5 filter responses have been checked against ADS and work as intended, EXCEPT the HPF filters don't work properly, SO USE HPF AT YOUR OWN RISK!

When you enter the passband frequencies for the filter, they are in Hertz. 10 GHz would be entered 1e10. The start and stop frequencies for the plot are entered in GHz. We plan to fix this inconsistency some day so you can enter them both in GHz.

### Design procedure

Much of the spreadsheet is locked so you can't mess with it, but the plots can be edited. The range of data is also up to the user, but keep in mind there are only 51 data points in the plots. The plot is unprotected, so you can mess with the axes as much as you want.

On the filter calculator pages (N3FILT, N5FILT), there are only six things you can enter, all of which are in blue boxes:

• whether the filter is low-pass (lpf), bandpass (bpf) or high-pass (hpf)
• the ripple in dB
• the passband frequencies F1 and F2
• the start and stop frequencies for the plot.

Note that once you have obtained a filter design, its frequency break points can be scaled in frequency by scaling the capacitances and inductors inversely (for 10X in frequency, multiply all values by 1/10).

We don't recommend using our free download above 2 GHz, unless you have the ability to calculate the parasitic elements into the

We also recommend that you restrict the ripple to 0.5 dB or less, that way you will be working toward a 2.0:1 or better VSWR in the passband (approximately -10 dB).

Remember, your lumped components will not always behave like ideal components, and this problem gets worse as you go up in frequency. You will need to look over data sheets and add in all parasitic items. These are not often given directly but can be computed from data such as the series resonant frequency of capacitors and the parallel resonant frequency of inductors. Unfortunately our free download can't help you with this, but it provides an excellent starting point for any lumped element filter design.

### Example 1: bandpass filter, 450 to 550 MHz

Suppose someone wanted you to design a bandpass filter at 500 MHz, with a passband of 100 MHz (450 to 550 MHz, with 30 dB rejection at 200 MHz and 1 GHz, and VSWR of 2.0:1.

Right away, you know that 0.5 dB ripple is required, because of the relationship between VSWR and ripple for a filter.

#### Determining filter order

Start with the lowest order filter, enter the passband and the ripple requirements. Adjust the start and stop frequencies for you particular filter; here we used 0.2 to 1.0 GHz. Remember, there are always 51 points, so it is important not to "waste" any of them outside of the passband and rejection points or the plot will miss some of the dips in S11.

If the passband is 450-550 MHz, we recommend adding some "guard band". We used 400 to 600 MHz in this example.

Below we show the response of a N=3 Chebyshev filter, with 0.5 dB ripple, 400-600 MHz. The network is shown graphically, as well as the capacitor and inductor values for tee and pi. Looks like the filter meets our rejection requirements, so there is no reason to go to a higher-order filter in this case!

Tee element values
C1= 1.662 pF
L1= 63.516 nH
C2= 17.454 pF
L2= 6.047 NH
C3= 1.662 pF
L3= 63.516 NH

Pi element values
C1= 25.406 pF
L1= 4.154 NH
C2= 2.419 pF
L2= 43.636 NH
C3= 25.406 pF
L3= 4.154 NH

#### Tee or pi network?

Now, which to choose, tee or pi network? (Ideally, the response will be the same.) We'd choose pi in this case, because the larger the inductor, the more trouble it can cause at microwave frequencies due to resonances and DC resistance. For the pi, the largest inductor is 45.6 NH, for the tee it is 63.5 NH

#### Resizing the components for available values

Next, you have to look into the availability of the inductor and capacitor values and enter these into the design. We like 0603 size components, so we check the DigiKey catalog. They offer AVX brand NPO capacitors, with the following values:

0.5 pF
1.0 pF
1.2 pF
1.5 pF
1.8 pF
2.2 pF
2.7 pF
3.3 pF
3.9 pF
4.7 pF
5.6 pF
6.8 pF
8.2 pF
9.0 pF
10 pF
12 pF
15 pF
18 pF
22 pF
27 pF
33 pF
39 pF
47 pF
56 pF
68 pF
82 pF
100 pF

For inductors, Digikey offers Susume thin film inductors of the following values:

1.0 nH
1.2 nH
1.5 nH
1.8 nH
2.2 nH
2.7 nH
3.3 nH
3.9 nH
4.7 nH
5.6 nH
6.8 nH
8.2 nH
9.0 nH
10 nH
12 nH
15 nH
18 nH
22 nH
27 nH
33 nH
39 nH
47 nH
56 nH
68 nH
82 nH
100 nH

Do you sense a pattern here? These values are called RETMA values, which dates back to 1957 and the Radio Electron Television Manufacturing Association, which is no longer around. But JEDEC (the Joint Electron Device Engineering Council), a part of the Electronic Industries Alliance (EIA) has a nice web page that will bring you up to date on the history of this.

Now you need to select RETMA components, or perhaps series or parallel combinations of parts from the RETMA list that give you an acceptable frequency response.

Now we have one more complication for you... in the filter spreadsheet, the response curve only "obeys" the tee filter (too bad if you wanted to play with the pi filter!) We rounded off the tee filter components to RETMA values:

Tee element values (RETMA)
C1= 1.5 pF
L1= 68 NH
C2= 18 pF
L2= 6 NH
C3= 1.5 pF
L3= 68 NH

Here's the slightly corrupted RETMA-value response. It took us one ham sandwich to design this filter.

#### Changing the system impedance

Suppose you want a 75 ohm filter? Just take the computed 50 ohm results, multiply the inductors by 1.5, and divide the capacitors by 1.5!