# Design a 1 GHz lowpass filter

I want to design a 1 GHz low-pass filter. I have tried to find a COTS lowpass filter at such high frequencies but I can't find one.

Hence, I have decided to design one using microstrip lines. So, can someone guide me through the process of designing microstrip based filters? or suggest any other alternative way to achieve this filter? I could not find a good tutorial online for the same. If such a tutorial exists, please give me the link.

Requirements for the filter:

1. Flat band response throughout the 1 GHz frequency range with a ripple of less than 2-3 dB.
2. Transition band of less than 50 MHz.
3. Attenuation in the rejection band of atleast 15 dB.
4. Attenuation in the pass band is at maximum 2 dB.
5. Input signal strength in the pass band is of the range of -10 dBm to -30 dBm.

Please note that I am not very strict on the above conditions but this is roughly the type of filter that I need.

Edit-1

This is the frequency spectrum of my input signal. I want to retain the information which is present upto 1 GHz frequency range. As you notice, the signal is already weak at higher frequencies, so the attenuation required at higher frequencies is much lower.

Please note that the photograph has been taken using a very bad camera, but the spectrum is from 0 to 4.5 GHz and hence 450 MHz/division on x-axis. The reference for the measurements in dB is 20 dBm and each unit on y-axis is 10dB.

• Try adjusting the "focus" thingy on your camera. – Olin Lathrop Mar 18 '12 at 12:55
• I have explained the dimensions/details below the photograph. If anything is unclear, please do let me know. – Neel Mehta Mar 18 '12 at 17:21

I can't answer this authoritatively but my gut tells me your spec is going to be "very difficult".

In particular, your transition band of 50 MHz is only 0.02 decades at 1 GHz, so you're looking for a drop of 714 dB/decade between your pass band edge and your rejection band. Which implies something like a 71-pole filter, requiring 71 active elements.

For reference, here's what can be done with a reasonable number of elements:

(Graph from TI's App Guide "Op-Amps for Everyone") The graph is in terms of "normalized frequency", meaning you can scale the filter elements in such a way as to make a frequency of "1" on the graph correspond to any frequency you choose, for example 1 GHz in your case.

At lower frequencies, we normally construct multi-pole filters by cascading 1 and 2-pole active sections to obtain some desired response.

At 1 GHz, you may, just be able to do that using rf amplifiers to buffer between stages. But more likely, you'll be stuck falling back on older techniques of constructing an LC ladder to get an approximation of the response you want. The problem with this technique is it tends to make the filter response more sensitive to small variations in the component values, caused by manufacturing differences or temperature sensitivities.

Of course, a combination of lumped and microstrip elements is also possible.

Edit: One reasonable design approach would be to use a tool like Matlab or Octave to see what kind of filter (Butterworth, Chebychev, etc, and how many poles) can come close to meeting your requirements. If you have access to a good library, look for a book with a title like "filter design handbook". This will give you lookup tables for the pole and zero locations of various types of filter of different orders. This will make it "easy" to calculate the response even if you don't have a high-priced tool like Matlab with the right toolbox to get the filter parameters from software.

Then, once you know where you want your poles and zeros, use a tool like ADS, or Genesys, or even SPICE, to design a filter using real L and C elements to create the mathematical response you optimized in Matlab. Then, be sure to do a sensitivity analysis to be sure the response stays in spec under normal variation of the part characteristics. Finally, depending on the L and C values you come up with, decide whether you want to implement some or all of those elements in microstrip instead of with discrete components. If you do decide to use microststrip, then use an rf design tool like ADS or Genesys (those are just two tools I've used myself, but there are others that could do this) to simulate and optimize the microstrip layout to achieve the behavior you want.

Another late note: You can see in the graph that for a Chebychev filter, the slope immediately after cut-off is steeper than the eventual slope of the skirt, so my statement of needing a 71-pole filter is probably too strong. But nonetheless, its clear you need at least 10 poles to meet your spec, and doing that with only passives is very challenging because of the stage-to-stage interactions and the required tight tolerances on the component values.

• Thank you very much for your very elaborate reply. I understand that it would be difficult to achieve such a small transition band. So, I have uploaded the frequency spectrum of my signal as Edit-1. Doesn't cascading multiple filters help in achieving better filtering? I can use amplifiers to boost the signal if the signal (within 1 GHz) is getting attenuated. – Neel Mehta Mar 18 '12 at 6:41
• @NeelMehta, Yes, cascading multiple filters can help, which is actually what Photon said in the first paragraph although it was written in lingo. He said you are going to need something Like a 71-pole filter. This can be roughly translated to 71 basic lowpass filters. A single filter can have many more poles then one, but an RC filter is a one pole filter. The point being though, think of how many filters that is and the complexity required. This is one of the reasons digital filtering is so popular when it can be used, it is very easy to have 71 datapoints in most cases. – Kortuk Mar 18 '12 at 17:25
• @thePhoton, For microstrip filters I would say this would be messy at best. At 1Ghz any Low pass filter I have designed has been too clunky to beat a lumped component filter. Not to say I do not think your advice is good, You probably know this, but wanted to mention it for the general crowds. – Kortuk Mar 18 '12 at 17:27
• @NeelMehta, Yes, cascading can improve the filter response. But 1. If you don't buffer between the stages then the cascaded stages start to interact with each other due to not maintaining 50 Ohm (or whatever) input impedance in the rejection band. 2. Multiple Chebychev (for example) stages can achieve greater loss in the rejection band, but at the cost of increased ripple in the pass band, which eventually will make you miss your ripple spec. As I did mention, of course you might use multiple 1 and 2-pole cascaded filters that work together to form some desired multi-pole filter. – The Photon Mar 19 '12 at 2:06
• @NeelMehta, Adding amplifiers will help (you notice I keep mentioning the need for buffering between cascaded stages), but also remember that an amplifier will not have perfectly constant gain, and the ripple of the buffer will eat in to your allowed ripple for the overall filter design. – The Photon Mar 19 '12 at 2:25

Would a coaxial low pass filter work for you? You might want to checkout Procom for example. Also take a look at the answers to the question 100W Low Pass Filter for drawings and additional information.