The Designer's Guide Community
Forum
Welcome, Guest. Please Login or Register. Please follow the Forum guidelines. Oct 23rd, 2017, 3:46pm
  HomeHelpSearchLoginRegisterPM to admin  
 
Pages: 1
Send Topic Print
Peaking in LC Circuit Frequency Response (Read 131 times)
Bean Nakamura
Junior Member
**
Offline



Posts: 19

Peaking in LC Circuit Frequency Response
Oct 02nd, 2017, 8:30am
 
Hello all,

Just a brief intro, so I’ve simulated the frequency response of an LC circuit with the output taken across the capacitor. After deriving the transfer function, I find that the equation is given by Vo/Vi = 1/(1-(W^2*L*C). From the equation I can find the f-3dB frequency which is given by f-3dB = 1/2*pi(sqrt(LC)). From the attached plot of the transfer function in dB20 scale it can be seen that as the frequency increases, the gain increases above 0dB and peaks at f-3dB before falling.

Questions:-
1) From the transfer function I am pretty sure that this circuit serves as a low pass filter as it passes anything lower than the f-3dB and attenuates anything after. What I don’t get is, why is the gain not constantly at 0dB below f-3dB? Why is there “gain”? Since this is a passive circuit, where is the gain coming from?

2) The way I understand this is that at lower frequencies, the impedance of L is lower and impedance of C is higher. Since the voltage is measured across C, the higher impedance across C translates to higher voltage and consequently gain. As frequency increases at the f-3dB frequency, the impedance of C and L are equal, hence the peaking. As the frequency further increases, impedance of L is higher than C, the voltage across C drops leading to lower gain. Am I analyzing this correctly?

3) From the waveform, the plot peaks at some value which is exactly at the f-3dB frequency. Is there an equation I can use to calculate the peak? Again, is the peaking the point where XL = XC as I said earlier?

4) I asked a postgrad and he briefly mentioned that the peak has been taken advantage of in RF IC circuits in some cases to increase performance in certain specs but he forgot the name of the papers and didn't quite explain the concept to me. Has anyone ever experienced using this f-3dB peaking to their advantage of has come across said paper? Would you mind sharing some insight or the name of the papers?

5) Can anyone point me to a good paper/book on the subject?
Any help is greatly appreciated. Thanks in advance!
Back to top
 

rfic_forum.PNG
View Profile   IP Logged
Ken Kundert
Global Moderator
*****
Offline

The Spectre

Posts: 2077
Silicon Valley
Re: Peaking in LC Circuit Frequency Response
Reply #1 - Oct 2nd, 2017, 11:28am
 
1) The peak occurs at resonance. Basically the circuit has a natural tendency to oscillate at the resonant frequency, meaning that the voltage will slosh back and forth between the capacitor and inductor.  The circuit is lossless, so any energy you manage to insert in the circuit stays in the circuit for ever and subsequent energy inserted simply adds to what is previously there. It is like waves in a bathtub: small movements if made at the right frequency can results in large waves.

2. yes.

3. The peak is infinitely large and narrow because your circuit is lossless.

4. There are many ways in which resonant circuit are used in RF circuits, but perhaps your grad student was revering to matching circuits. I have no good references, but there must be many on the web. Search for matching or matching networks.

5. I can recommend my paper on phasors.

-Ken
Back to top
 
 
View Profile WWW   IP Logged
Bean Nakamura
Junior Member
**
Offline



Posts: 19

Re: Peaking in LC Circuit Frequency Response
Reply #2 - Oct 8th, 2017, 6:16pm
 
Thanks for your input Ken!
I will definitely check out your paper.
Back to top
 
 
View Profile   IP Logged
Horror Vacui
Community Member
***
Offline



Posts: 47

Re: Peaking in LC Circuit Frequency Response
Reply #3 - Yesterday at 12:07pm
 
I am not sure where are you from. You can look in any old physics/electronics text books.I had series/parallel RLC cirucits in my grammar school textbooks (not in engineering detail, but still it was there), and I learned about it in the 21st century.
Or any textbook which is about RF design. These RLC circuits are very important and useful for impedance transformation, which is very important at high frequencies where the gain is limited.
So after you read Ken's paper there are plenty of available books about it.
Back to top
 
 
View Profile   IP Logged
Pages: 1
Send Topic Print
Trouble viewing this site? Copyright © 2002-2014 Designer's Guide Consulting. 'Designer's Guide' is a registered trademark of Designer's Guide LLC. All rights reserved.

Our colleges are not as safe as they seem. Sexual assault is pervasive and the treatment of the victim by the adminstration is often as damaging as the assault: Campus Survivors, Campus Survivors Forum.

Some of our other sites that you might find useful: QuantiPhy.