how to realize a network and the values of its elements from a mathematical function?

Thread Starter

sara yu

Joined Sep 24, 2015
9
I have homework problems to solve on network synthesis,in which I don't have enough background knowledge, I need help with figuring out the elements and their values in a the network when a transfer function is given.
In the file uploaded,there is a simple example, from which I could not understand how the values from the equation are assigned to the elements in the network.

Also I am uploading a problem from my HW. Any help in this domain will be appreciated.
Thanks,
Sara
 

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WBahn

Joined Mar 31, 2012
24,684
What kind of networks are going to give you a second order transfer function?

Is the transfer function for a low-pass, high-pass, band-pass, or band-stop filter (or something else)?

You need to show YOUR best attempt to work YOUR homework problem. It doesn't have to be correct, but it serves as the starting point for discussion.
 

Thread Starter

sara yu

Joined Sep 24, 2015
9
Thank you WBahn for your response. Before attempting my HW problem I am following some lectures from the videos and reading through pdf docs, to get the basic understanding of these concepts in order for me to apply. I am still not sure but could understand a little. Here is what I got in the attachment below, I will sure apply it to my HW problems, just because of time constraints, I posted this for some help with the concept. Will post any of my work to solve problems in HW too.
 

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WBahn

Joined Mar 31, 2012
24,684
I can't make out very much of your work -- unlike most picture of the attachments here (which tend to be huge files that are 100x too big), you need to increase your resolution and also take the picture looked more straight down at the work.

Your first step is to examine the transfer function and see what kind of filter response it has. If nothing else, plot the magnitude of the response as a function of frequency.
 

Thread Starter

sara yu

Joined Sep 24, 2015
9
sorry for the image size and quality.. I just started working on my HW,attaching that here along with the modified earlier attachment.
From the problem I see -1 and -2 as poles,that are close to 0 so it is a slowly decaying function... c exp (-t) & c exp(-2t)...
 

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RBR1317

Joined Nov 13, 2010
489
so it is a slowly decaying function... c exp (-t) & c exp(-2t)...
OK, so the mystery circuit must have 2 RL or RC time constants. What about the behavior at DC, ω=0? If the circuit has zero attenuation at DC, what component must connect the input to output? If the DC attenuation is infinite, what component must be inline? If the DC attenuation is fixed at some non-zero value, would that form a DC voltage divider with the output resistance? The DC performance should narrow down the range of possible circuit candidates.
 

Thread Starter

sara yu

Joined Sep 24, 2015
9
Thank you RBR1317. I am in to EE course from a Physics background . I am trying to learn some and then recollect those that I have learnt in the past.So my questions might sound kind of basic.
Mystery circuit must have 2 RL or RC time constants .Do you say this because there are two poles in the given transfer function?Also, your guiding questions on DC performance makes me think that questions like this (HW)could be answered by inspection with thorough basic knowledge,Which is interesting and I want to be able to do that. However, I need to work out the math to realize the circuit for my HW.
Thank you again.
 

RBR1317

Joined Nov 13, 2010
489
Mystery circuit must have 2 RL or RC time constants .Do you say this because there are two poles in the given transfer function?
Well, I could say "Yes", but the truth is I'm pretty rusty in my network synthesis skills. The main reason is that you calculated the time domain response would have two exponential decay components, and exponential decay comes from an RL or RC time constant. So I tried analyzing some possible RL & RC circuit configurations and found only one that could satisfy the specified DC response. Maybe you will find something different, but there are a limited number of configurations for second-order passive circuits - and fewer still that can meet the DC response here.
 

WBahn

Joined Mar 31, 2012
24,684
Thank you RBR1317. I am in to EE course from a Physics background . I am trying to learn some and then recollect those that I have learnt in the past.So my questions might sound kind of basic.
Mystery circuit must have 2 RL or RC time constants .Do you say this because there are two poles in the given transfer function?Also, your guiding questions on DC performance makes me think that questions like this (HW)could be answered by inspection with thorough basic knowledge,Which is interesting and I want to be able to do that. However, I need to work out the math to realize the circuit for my HW.
Thank you again.
Look at the transfer function and describe how it behaves as a function of frequency? What is it at DC? What is it at very high frequencies? How does it change with frequency?
 
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