Help in the conversion of circuit to a T section Bandpass

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Hi Guys,

I have attached here a filter i acquired from one of my professors. From first glance, I saw that the presence of the inductor and capacitor at the two ends seem to mimic the Tee section bandpass filter. Since I am trying to solve for the bandwidth to be used from the formulas available, i was wondering if what i am doing is in the right direction or if anybody can propose a solution?

Currently this is what I have...
upload_2018-10-12_16-2-39.png

I am not sure if I am able to justify the parallel arrangement of the two 33n inductors with the 8.2n inductor.

Thanks for any advice and help!!
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
upload_2018-10-12_16-4-14.png

upload_2018-10-12_16-4-36.png

Attached here is also the schematic i draw inspiration from which i assume is the basis of the filter. Thank you to whoever took the time out their friday to answer this :)
 

MrAl

Joined Jun 17, 2014
6,485
Hi,

Just curious, is the output load impedance supposed to be 50 ohms too?
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Hi sir! Thanks for taking the time to reply! Actually the output goes into an RF switch and the impedance attached is actually 20kohms
 

The Electrician

Joined Oct 9, 2007
2,737
What is your ultimate goal here? Are you required to find the cutoff frequencies (f1 and f2) of the filter you got from your professor?

You could proceed in a couple of ways. You could just derive the transfer function of the given filter and from that you could calculate f1 and f2 as the frequencies where the filter gain is .707 times the midband gain (or whatever else is your criterion for the cutoff frequencies). This method would not involve trying to convert the given filter into a T section filter.

Or you could try to convert the transfer function into the equivalent series and shunt arms of a T network, and then determine f1 and f2 from the formulas given for the theoretical T section circuit.

So what is your goal? Are you required to find the equivalent T section, or can you use whatever method you wish to achieve your goal?

For a start, you need to find the transfer function. For the T section to behave according to the theoretical formulas, it must be driven by and loaded by Zo. You should probably initially calculate the transfer function assuming 50 ohm source impedance and 50 ohm load.

By the way, you never did come back to the other thread: https://forum.allaboutcircuits.com/threads/help-on-node-analysis-for-filter-interpretation.152941/

where you were having trouble setting up the nodal equations. If you are going to have trouble with that here, we can help you.
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Hi guys! Sorry was away for a while with modules piling in. I can utilise any method possible but i assumed that the generalisation of it to be a T filter would be easier. I was mistaken i guess. Additionally, i went to look at the schematic again and realised that the termination impedance is actually 50 ohms too! Sorry for the error in disseminating information.

I am just unsure of the design of the filter since i have not seen a filter being made in this way. Thus, i am abit stunned with how to proceed with the determination of the cut-off frequencies moving forward. If anybody is willing to push me to a headstart, i would be more than happy to work on it again.

Thank you so much and i apologize for the disappearance and lack of updates!
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
i did the simulations on LTSPice and i got the output as shown...

upload_2018-10-26_7-2-28.png

upload_2018-10-26_7-2-44.png

which corresponds nicely with the frequency she is expecting to churn out from the filter used. However, mathematically, i am finding it difficult to prove the explanation.
 

Attachments

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
HI thanks for the reply! Assuming i have the transfer function alr, which i am working on, how does it translate to a working frequency cut-off for the bandpass filter? Additionally, I can also do this for a perfect T section filter and attaine similar results right?

Thanks again sir!
 
HI thanks for the reply! Assuming i have the transfer function alr, which i am working on, how does it translate to a working frequency cut-off for the bandpass filter? Additionally, I can also do this for a perfect T section filter and attaine similar results right?

Thanks again sir!
Once you have the transfer function, you can solve for the frequencies where the output voltage is SQR(.5) times the midband value.
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Hi, thank you once again for all your help so far. I did a node analysis and this is what i came up with at nodes signified by the black dot.
However, i got a weird transfer function from my solver,
being
-(149803917826417560712640015970611494912000000000000000*S*V1*(5100155801499217*S^2 - 944473296573929042739200*S + 188894659314785808547840000000000))/(4401312662811810507569611625986352939085711368539721060538603820000000*S^3 + 6080438531522487234392879237199407690483535567941175127883554217636011426930191*S^2 + 1004894268092706158461120781268848589582846809639485331856640338369929993771393063321600*S + 172543658669764108903466370945486749409498014996342053055389865223328718754278612664320000000000).
Assuming i input a 1V AC input voltage, i can just let the equation stated be equal to 0.707 and solve for S in matlab too right?

However i am getting an error. Hopefully, you can clarify it for me! Thank you so much sir for all the help! :)

upload_2018-10-26_10-57-38.png

upload_2018-10-26_10-59-19.png
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
an additional question for anybody who is willing to share, upon first glance of this filter, i had an impression that it was a t section bandpass based off the arrangements of the series components. However, i realised that it wasnt when it did not fulfil the formulas to be used.

Thus, i would also like to ask if i were to explain this filter, could i say that it is a tsection bandpass filter based off the series components arrangements?

I am not sure what to make out of the t arranged 33nH, 8.2nH and 33nH inductors in the middle and i am not sure how i would explain it to a fellow mate if he asks. What is the purpose there?

My initial guess was with regards to standard components not being available soit was put to make up for the value. Any additional insight would be really helpful. Thank you!
 
The designators you've labeled on the schematic (I've circled in red) don't correspond to how you used them in your equations.

Redo them like this:

upload_2018-10-26_10-59-19.png

Note that V4 is the same as Vout. Write your equations using Vin, v1, v2, v3, Vout. If you get an error, tell me what the error is.
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Hi Sir,

I have made the necessary changes. Called out the VOUT to solve for S since I am assuming VIN is a 1V input.However, i got an error...
upload_2018-10-26_14-14-26.png

the outputs are weird and give me this message...
upload_2018-10-26_14-16-44.png
upload_2018-10-26_14-15-34.png

edit: Should the equation be done in that format? Should i be expecting just an integer? I tried using vpasolve and it still gave me an unknown in the form of z as seen above in the answer...
Thank you again for your help and clarification. Your help is really amazing!
 

Attachments

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Update: I inputted Vin to be 1 and ran the simulations again. I used the function vpasolve on the VOUT equation attained and set boundaries to only be positive values.

I got none :(
upload_2018-10-26_14-30-24.png
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Sorry again but update:
Realised i got the S parameter. Went to convert it to f and i got only 3 positive values...
upload_2018-10-26_14-39-35.png
corresponding to the 1st, 4th and 5th value.
they correspond to 26 MHz, 28MHz and 24.5Mhz... not sure if its correct but finally see some values lying close to the actual frequency wanted...
 

MrAl

Joined Jun 17, 2014
6,485
Hello,

Your graphic cuts off the top of the response curve, which may be important. Check that out.

You know you have a low pass filter if a lot of low frequency signals are passed and a lot of high frequency signals are attenuated usually by a lot.
You know you have a high pass filter if it passes high frequencies and attenuates low frequencies.
You know you have a band pass filter if the passes intermediate frequencies and attenuates low and high frequencies.
You know you have a band stop filter if it attenuates intermediate frequencies and passes high and low frequencies.
Those are the most common.

I get a shallow snake tongue response roughly around 25MHz. See if you can reproduce this.
 

Thread Starter

Muhammad Salleh

Joined Oct 5, 2018
34
Hello,

Your graphic cuts off the top of the response curve, which may be important. Check that out.

You know you have a low pass filter if a lot of low frequency signals are passed and a lot of high frequency signals are attenuated usually by a lot.
You know you have a high pass filter if it passes high frequencies and attenuates low frequencies.
You know you have a band pass filter if the passes intermediate frequencies and attenuates low and high frequencies.
You know you have a band stop filter if it attenuates intermediate frequencies and passes high and low frequencies.
Those are the most common.

I get a shallow snake tongue response roughly around 25MHz. See if you can reproduce this.
HI sir, were you referring to the LTspice simulations? Unfortunately I will only be able to view that as i go back to my school's laptop as i do not have the cpacity in my macbook (sadly) to have LTspice and run the simulations.

from my memory, i remember it being a bandpass filter from the simulations on LTSpice mainly because the values peaked at the frequency desired( ~24MHz) and everything else was attenuated... is my understanding wrong sir?

Thank you again!
 

MrAl

Joined Jun 17, 2014
6,485
HI sir, were you referring to the LTspice simulations? Unfortunately I will only be able to view that as i go back to my school's laptop as i do not have the cpacity in my macbook (sadly) to have LTspice and run the simulations.

from my memory, i remember it being a bandpass filter from the simulations on LTSpice mainly because the values peaked at the frequency desired( ~24MHz) and everything else was attenuated... is my understanding wrong sir?

Thank you again!
Hi,

No you were not wrong, i thought you had asked how you can tell if you have a bandpass or other filter back in this thread.
Since you know it is a bandpass, that's good :)

There are actually two peaks from what i see from a transfer function graphing.
The two peaks are separated by a dip but the dip does not go too far down. So i called it a snake tongue.
Your graphic seems to cut off at the top so you may not see this and it may look like one peak alone.
Maybe not extremely important, but i thought you would want to know.
 
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