Building a physical circuit from a transfer function

[barriboy]

I am trying to build a high frequency analog filter. I don't have the specs quite yet, but I do know how to create the transfer function. The trouble is, once I have that, how do I go about making this into a physical circuit?

All the online stuff I can find is either digital or low frequency (like audio) active filters. For the frequencies I will be using (around 1.3 GHz), these will not work. I have designed many digital filters in Matlab before, but I have never had to actually build a circuit.

I can do some pretty basic single resistor/capacitor circuits to get run of the mill filters, but I fear these will not have the performance I need. There are a few analog filter textbooks at the library, but they are all checked out at the moment. Does anyone have any recommendations for good analog filter design books (that include high frequency applications?)

Also, any ideas how to test this once I create it? I can't imagine I can find a function generator that will give me gigahertz range.

Thanks!

 

[marcusl]

Practical filters are designed by choosing a type and structure, rather than a frequency response, and finding the number of poles required to meet the requirement. Component values (or stripline parameters) are then easily computed. The classic text is Mattaei, Microwave Filters, Impedance-Matching Networks, and Coupling Structures. Testing is usually performed with a network analyzer. If you don't have access to this kind of equipment, perhaps you can look into ham radio books. Perhaps there are some homebrew approaches to microwave test equipment?

 

[barriboy]

Hey, thanks for the reply. I will look into that text. Unfortunately I don't yet know the specs, only the general idea of what I am being tasked to do. I was thinking Chebyshev or Butterworth, but given that I still don't know what I am going to be doing exactly, I'm not sure which of them would be better suited to my needs.

I am going to need to make a bandpass that passes 1.3GHz, but don't know what my bandwidth should be. I will also be making a low pass later on with as of yet undefined parameters.

Basically I have a time crunch and need to finish this and something else in a few months, but due to bureaucracy and lawyers, I won't be allowed into my lab for some time. I just want to be able to walk into the lab with a clear idea of how to go about building the circuits.

 

[psparky]

This should do you right here...bandpass circuit.

Pick your resistors...then plug in your capacitor numbers keeping in mind that your breaks happen at ω=1/(RC).

Clear picture of it right here...

http://www.allaboutcircuits.com/vol_2/chpt_8/4.html

 

[barriboy]

psparky, I had seen those circuits, but I am concerned that they won't work for me. For example, if I wanted to make my break points 1.29 and 1.31 Ghz, The resulting capacitors for a 1k Ohm resistor would be 775 and 763 fF. The difference between them is so small that I imagine the circuit wouldn't function properly, given the variance of capacitor values. Does this just mean that the bandwidth in this example is far too low to be realistically made?

 

[f95toli]

At 1.3 GHz you are probably above the limit of what can be done with discrete components, meaning you need to design a proper microwave filter; which is unfortunately far from trivial.

If you are new to microwaves I would recommend checking out Pozar's book (this is the book everyone uses), it has a chapter where he discusses how to go from a filter function to a practical circuit with stubs etc.

 

[psparky]

psparky, I had seen those circuits, but I am concerned that they won't work for me. For example, if I wanted to make my break points 1.29 and 1.31 Ghz, The resulting capacitors for a 1k Ohm resistor would be 775 and 763 fF. The difference between them is so small that I imagine the circuit wouldn't function properly, given the variance of capacitor values. Does this just mean that the bandwidth in this example is far too low to be realistically made?

I hear ya.

Make a sketch of your bode plot. Graph near your 1.30 ghz...ω= 2π*1.30 ghz
Graph the high pass and low pass in this area.
Your transfer function for the high as you know is jωRC/(jωRC+1)
For your low it is 1/(jωRC +1)

Plug in your numbers for your RC...and pick your ω for each. You will obviously end up with a vector with magnitude and angle. Play with the numbers...see what you get.

I'm not sure exactly what your doing with this frequency of 1.3 ghz...but I have a feeling you will want steeper than 20 db/deca. Try it with the single poles first and see if it fits your criteria.

 

[barriboy]

f95toli, that is what I had feared. I am looking at some RF filter design guides, but most of them still seem to be focused on frequencies lower than what I need them for. Is the book Microwave Engineering by David Pozar?

Thanks to you and everyone!

 

[psparky]

At 1.3 GHz you are probably above the limit of what can be done with discrete components, meaning you need to design a proper microwave filter; which is unfortunately far from trivial.

If you are new to microwaves I would recommend checking out Pozar's book (this is the book everyone uses), it has a chapter where he discusses how to go from a filter function to a practical circuit with stubs etc.

btw...up to what frequency will your typical RC filter behave like it's transfer function?

 

[marcusl]

barriboy, yes that is the Pozar book. It is excellent.

Given that you're a newcomer to MW filters, and lack test gear, I suggest purchasing a filter from K&L, Lark, or the like. These vendors specialize in building one-off custom filters. You will spend less on the filter then on test equipment rental fees and the salary to you build yourself into a design expert, and you'll have a component that will work perfectly the first time.

psparky, your comments indicate a substantial lack of knowledge regarding microwave techniques. Suggest you leave the advice to those who have that knowledge and experience. Questions, on the other hand, are always welcome.

 

[psparky]

barriboy, yes that is the Pozar book. It is excellent.

Given that you're a newcomer to MW filters, and lack test gear, I suggest purchasing a filter from K&L, Lark, or the like. These vendors specialize in building one-off custom filters. You will spend less on the filter then on test equipment rental fees and the salary to you build yourself into a design expert, and you'll have a component that will work perfectly the first time.

psparky, your comments indicate a substantial lack of knowledge regarding microwave techniques. Suggest you leave the advice to those who have that knowledge and experience. Questions, on the other hand, are always welcome.

Absolutely, I wrote my post 2 minutes after yours...in other words I didn't read yours before I wrote mine.

Didn't know RC's fall apart at mega frequencies.

Again...about what frequency does and RC filter no longer follow its transfer function?

 

[yungman]

Hey, thanks for the reply. I will look into that text. Unfortunately I don't yet know the specs, only the general idea of what I am being tasked to do. I was thinking Chebyshev or Butterworth, but given that I still don't know what I am going to be doing exactly, I'm not sure which of them would be better suited to my needs.

I am going to need to make a bandpass that passes 1.3GHz, but don't know what my bandwidth should be. I will also be making a low pass later on with as of yet undefined parameters.

Basically I have a time crunch and need to finish this and something else in a few months, but due to bureaucracy and lawyers, I won't be allowed into my lab for some time. I just want to be able to walk into the lab with a clear idea of how to go about building the circuits.

As an EE, I never even look at all the transfer functions for filters. The important thing to know is the bandwidth and what is the off band attenuation characteristic. Then you want to know the pass band ripple. The first two are the most important. From design experience, I need a filter to attenuate the unwanted frequency that might swamp the frequency of interest. The difficult thing is to choose the right filter to get the attenuation of the off band frequency.

Say if your center frequency of interest is 1.3GHz, and there is a large peak at 2.4GHz( common). This is less than 2fc and you have to choose the correct type of filter and the minimum number of stages needed.

It is more important for you to get a book or down load some articles on the frequency response of like Bessels, Butterworth, Chebichev( spelling) etc. Look at the graph to find the right one. At your frequency, active filter is out, mainly is passive LC filters. At your frequency, distributed transmission line frequency is a little big. So stay on the discrete LC filter.

After choosing the filter and number of stages, then learn from the table how to translate the normalize number to a real filter. No theory involve, just look up the normalized component values and translate using the formulas provided in the article. The theory of the filter is much more difficult than just making a working filter. I did so many filter just by cook book implementation.

 

[AlephZero]

Again...about what frequency does and RC filter no longer follow its transfer function?

A filter always follows its transfer function. The problem is that you are confusing the transfer function of the real filter with a simple model (equation) based on ideal components. At GHz frequencies, most "jellybean" components don't behave anything like ideal ones.

If you ignore the fact that real components are not ideal, you can easily design filters that "don't work properly" at 1.3 kHz, let alone 1.3 GHz.

 

[marcusl]

Absolutely, I wrote my post 2 minutes after yours...in other words I didn't read yours before I wrote mine.

Really? My post appeared at 9:16 pm, yours at 8:10 the next morning.

Didn't know RC's fall apart at mega frequencies.

That is exactly my point. Please don't give advice in areas where you lack knowledge/experience.

 

[yungman]

RC and LC filter work for 1.3GHz, we used them even at 1.9GHz. You really have to take parasitics into consideration when you do that though.

Anything higher frequency, it will get dicey! distributed element start to become more of a choice.

 

[psparky]

Really? My post appeared at 9:16 pm, yours at 8:10 the next morning.

That is exactly my point. Please don't give advice in areas where you lack knowledge/experience.

Relax, It's a discussion of a filter. Not a 12.5 KV switchgear hook up. I shared some mathematical equations of ideal components.

Thank you for teaching me how these non ideal components don't work like their mathematical equations.

 

[marcusl]

Ok, I'll relax...

 

[yungman]

To the OP, one thing I forgot to mention, even at 1.3GHz, you have to be careful about the impedance of the driving circuit or the receiving circuit of the filter. Do not take for granted that the input and output impedance is constant through out the band of interest or the frequency you want to reject.

You are in the RF world, you really cannot separate different parts of the circuit like in the lower frequency. Any change of the source and termination impedance of the filter will change the characteristics of the filter and you can't count on simple filter design.

You have to have a clear definition of what frequency you want to pass, what frequency you need to avoid. Also the amplifier driving the filter has Zout, input that the filter drive has a Zin. You need to know that when you design a filter. That's where the RF world comes in...The S parameters and all.

If you really need help, you should post the circuit, the components you use and all. Nothing is easy even at 1.3GHz. Sometimes a multi pole filter may not even be the best way to go. I usually design these kind of stuff using the smith chart and verify with simulation. You want to get into these stuffs, the book by David Pozar is a very good book if you have a good math and physics background. It's not exactly for the weak of heart.

Hope I don't discourage you too much. If you just want one filter to do a job, you might want to look at some or the ready made band pass filters in places like DigiKey online. I am not familiar with those, I just know they have specific BP filters in one small little package.

http://www.digikey.com/product-search/en/filters/rf-specific/3408632?k=band%20pass%20filter

Can't help you on this, never use one before.