# Designing an active band pass filter at VHF

#### alex1234

Joined Jul 10, 2010
7
I am working on a mini project in which I have to design an active narrow band pass filter of 4th order (I chose butterworth filter because we need to avoid ripples and also have a steeper response, this is satisfied by butterworth as chebyshev gives ripples and Bessle's has linear slope.) which will work at 10MHz-30MHz,having a passband of 1MHz.
Also I have used uA741 which is included in PSPICE library.

This filter is supposed to be a variable (but that is to be done later.)
However I am stuck on first step, I used the basic formulas and got values of resistors. I had to make capacitor values low such that resistor values would be significant.

I was able to design sucessfully for center frequency on 1kHz,but the same method I guess doesnot work for 10-30MHz.
From this what I could think of is the capacitors(values in picofarads) change their characteristics at VHF.

Here is what I did for center frequency of 1kHz.(kindly see the attachment)

fc=center frequency.
A=Gain(Assumed A=1)
Q=Quality factor(Assumed Q=100)
C1=refer schematic.
C2=refer schematic.
Using same formulaes, I got the resistors for fenter frequency of 10MHz.
C1=C2=10pF.

R1=Q/(2∏*fc*C*A)=159.15kΩ
R1=Q/(2∏*fc*C*(2Q^2-A))=7.958Ω
R3=R4=Q/(∏*fc*C*A)=318.309kΩ

for attached images (sch.png=schematic for 1kHz cutoff, 1Khz.png=response of sch.png, and bfp.png=response for 10Mhz bpf_r1.png is schematic for 10Mhz)

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#### SgtWookie

Joined Jul 17, 2007
22,221
For starters, the 741 opamp will be completely useless at those frequencies. You require a very fast opamp, as that's the only way you're going to get the bandwidth you need.

Look at current-feedback opamps. Video opamps are current feedback, and they operate happily in the 50MHz and up region. Look for an amp that's stable with Av=1 (a gain of 1)

Small ceramic capacitors do have parasitics, but until you're actually in RF territory, the parasitics are very slight. Anything below 20MHz is still basically DC.

You might look at using varactor diodes for tuning. If additional capacitance is required, you can use several varactor diodes in parallel.

#### Wendy

Joined Mar 24, 2008
22,545
The main purpose for active filters is to make filters that would normally require huge inductors. For high frequencies (I would define that as anything over 100Khz) a conventional LC filter works well. Active filters basically simulate LC filters with really large inductors.

The 741 op amp is almost useless for anything of 10Khz, and that is pushing it. At 10Khz it has a gain around 100 (unity at 1Mhz), and there are other op amp specs that affect frequency responses it is even worst at (I'm thinking of something called slew rate). It is good for DC (though there are much, much better parts) and for teaching op amps, where all those terrible specs are good learning opportunities.

#### alex1234

Joined Jul 10, 2010
7
First of all I am thankful to both of you because you took some time (and pain as well) to reply to my question.

I have replaced the ua741 by LMC6464.
It gives be good characteristics as a band pass filter, but is not exactly at 10MHz.

I tried nearly 60-80 opamps of high speed and large bandwidth, but I get absurd responses, the most common of them was some what similar to that of high-pass filter. Since i am just a beginner,i am unaware of the things that cause this. So if any one can enlighten me on this,it would be really very helpful.

Also, I want to ask whether the designing formulas change according to op amps.(In exams we have same procedure,and ua741 give tolerable characteristics to it.)

here is the new schematic and response.

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#### SgtWookie

Joined Jul 17, 2007
22,221
Did you remember to take into account the input and output parasitics of the opamp?

Look at a datasheet to see what they are.

Also keep in mind that opamps have propagation delays; what goes in one end doesn't come out the other end immediately.

Did you notice the load specifications in the datasheet?

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#### Wendy

Joined Mar 24, 2008
22,545
Is this homework? You would be much better designing a LC filter followed by an amplifier (which would also provide excellent isolation).

You want a 4th order bandpass, adjustable 10Mhz to 30 Mhz with a pass band of 1Mhz.

I'll be honest, I don't think this can be done using active filters, which is why I mention conventional designs. Due to the wide range of adjustability I think it will be quite hard using conventional techniques too. You have a Q difference of X3 end to end with the problem as stated.

There are reasons while super heterodyne was invented, radios covering a band that wide have similar problems. So they figured out a way to drop the frequencies to a common IF, so the bandwidth stayed the same no matter what the receiver was set for.

#### bertus

Joined Apr 5, 2008
21,534
Hello,

If you want to design a filter for that frequency, you better use LC circuits.

By the way, 10 - 30 Mhz is still HF and not VHF, see the table:

Rich (BB code):
Very Low Frequency       VLF 3 kHz - 30 kHz
Low Frequency            LF  30 kHz - 300 kHz
Medium Frequency         MF  300 kHz - 3 MHz
High Frequency           HF  3 MHz - 30 MHz
Very High Frequency      VHF 30 MHz - 300 MHz
Ultra High Frequency     UHF 300 MHz - 3 GHz
Super High Frequency     SHF 3 GHz - 30 GHz
Extremely High Frequency EHF 30 GHz - 300 GHz
Bertus

#### alex1234

Joined Jul 10, 2010
7
Thank yu for all replies,and I agree that range is HF and not VHF.
Actually its a mini project. Every year we have one project for which we have 3 months to complete.
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Basically this band-pass filter would be connected to some oscillator which has tunable frequency.(Making this oscillator is some other person's job,not mine.)then this oscillator would be tuned to some frequency,and then bpf will show which freq its passing,by adjusting the center frequency.Thus this should be narrow bpf and should be tunable.
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I took you suggestions on r-l-c filter, implemented it,but then if I try to increase the Q(quality factor),then the system oscillates(ζ<<1),this will make my bpf to be unstable.(which may be in range of Mhz, for Q=100,I get about 10MHz oscillation frequency. ) But then for Q=100 I get a very good response,and have to bother about less number of cascades.
-------------------------------------------------------------------------
I chose simple r-l-c parallel ckt.
I searched for a way for improvement in both Q and ζ,but I guess one has to make a compromise in between them.
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I was very happy with my results from R-L-C circuits,unless my project manager told me that it should be an active filter.(I designed R-L-C ckts and got the response.)
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So again the same old story, This time I chose a higher side op amp which has current-feedback. that is OPA658(OPA658X/BB in PSPICE library.)
I chose the center frequency as 10MHz,C1=C2=100pF.
and using the formulas got R1=R2=159Ω R3=R4=318.3Ω

I included the source resistor of 50Ω(referred from data-sheet.)
But the graph is not matching to that of bpf.The slew-rate,and GBP matches perfectly as requirement,Its very wide band opamp and has a very high slew rate. I also took into the parasitic capacitances of the OPAMP. but nothing is improving in frequency response.
The schematic remains the same,just few things added here and there,like source resistance and load resistances.
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I have couple of questions now

1.What is better active filter or passive filters?

2.If passive filters can satisfy needs of the filter designer, then would it not be convinent to design a filter that is needed,and just connect a Instrumentation ampliier before it?

The instrumentation amp,will remove the noise and filter will do its job,then why is it,that many people go for active filter designing?

#### Wendy

Joined Mar 24, 2008
22,545
They are fairly equivalent, I've stated the reasons why active filters are used for audio and lower. You don't need a instrumentation amplifier, just a amp with good rejection between output an input, likely they will be sharing a ground (unless this is a design criteria).

The amplifier keeps the output impedance of the filter constant. This is critical for any non-active filter, a variable impedance or even if the impedance is off from calculated value can change the filter drastically. An active filter doesn't have this problem, because the output impedance is very close to 0Ω (part of the nature of op amps). Traditional designs usually add something like a 6db attenuator to get the output impedance as close to nominal as can be done, then add an amplifier.

I have a lot of experience in this field (I was a lead tech at Collins Radio), I have never heard of an active filter being used much over 1Mhz. I do have to a the cravat that this was over 10 years ago however, technology could have marched on without me.

One last thing, you have a conventional filter, it can take hours or even days to tune, and this assumes good test equipment. Some of the stuff I started using in the 70's was not very good, it did the job. The later stuff added equalizations that made the job much easier.

#### alex1234

Joined Jul 10, 2010
7
Thank you again.
Now I have a fairly fast opamp which can operate till 50MHz.
I have tried various topologies,but not able to decide which topology is best for this application(Very High Q).

I tried the following:
Akerberg-Mossberg.
Sallen-Key.
LeapFrog.
Fliege.
MFB.
KHN.
MB.

So can any one please suggest me the best topology that I could use for a very narrow band pass filter,another criteria is to make it programmable from 1MHz-50MHz.