How Can I Find Resonance Frequency and Create a Schedule for Input Resistance?

[builder_user]

Homework Statement

Find resonance frequency and build schedule(google translator) for input resistance(or input conductivity)

Homework Equations

K1xL1/L0=70
K1xL2/L0=60
K1xL3/L0=76
K2xC1/C0=80
K3xC2/C0=50
K3xC3/C0=60

The Attempt at a Solution

C0=1mkF
L0=1millihenry

What do I need to do at all??What are K1,K2,K3?

 

[gneill]

If you don't have values for K1, K2, and K3, then it would appear that you can only find a symbolic result for the input impedance and the resonant frequency. The algebra will get a bit nasty!

This is the first time I've seen component values specified in this way, so I'm not sure what significance, if any, it might have. It would be nice if the simplified expressions for the impedance and resonant frequency turned out to involve some simple relationship between the K's and C0 and L0, but I doubt that this will be the case!

 

[builder_user]

I think symbolic results will be enough.Besides Mathcad can solve equatations in symbolic form.

 

[gneill]

I think symbolic results will be enough.Besides Mathcad can solve equatations in symbolic form.

Well, I look forward to seeing your results!

How do you plan on finding the input impedance?

 

[builder_user]

Well, I look forward to seeing your results!

How do you plan on finding the input impedance?

I think I'll sum all resistance

S=((Rc2+Rl3)*Rl2)/(Rc2+Rl3+rl2) - sum resisntace C2 L3 L2

S1=S+C1 - sum resistance C1 C2 L3 L2

(S1*L1)/(S1+L1) - sum resistance

 

[gneill]

Strictly speaking, the term to use when reactances are involved is impedance rather than resistance.

Your method of finding the overall impedance is fine. Another method, which can be handy when the circuit is complicated and tricky to solve that way (say of there are some Delta or Y configurations involving reactances) is to place a fictitious voltage source at the input and solve for the current it drives into the circuit. The impedance will then be the ratio of the voltage to that current. This allows you to use the usual KVL loop approach -- and you only need to solve for the current in the first loop.

 

[builder_user]

But if use my method, what do I need to do next?Add voltage source and find currents?

 

[gneill]

But if use my method, what do I need to do next?Add voltage source and find currents?

Resonance occurs when the imaginary part of the impedance goes to zero. In this case, since there are only reactive components, the impedance has only an imaginary component.

Set the expression for the imaginary component of the impedance to zero and solve for the frequency.

 

[builder_user]

It means for example3a+9ib---> 9ib=0?

 

[gneill]

It means for example


3a+9ib---> 9ib=0?

Yes, or if you like, drop the 9i which is constant and find when b = 0.

 

[builder_user]

I got such strange result

 

[gneill]

Some of your substitutions didn't "take". In particular, you don't have S and S1 on the LHS of assignment statements.

 

[builder_user]

Some of your substitutions didn't "take". In particular, you don't have S and S1 on the LHS of assignment statements.

I've reloaded my previous post

Now It seems that imaginary component is all the result

 

[gneill]

Sorry, I can't read Mathcad 14 worksheets. My version is Mathcad 2000.

 

[builder_user]

what format? *.mcd?

 

[gneill]

Yup. File --> Save as --> Mathcad 2000 Worksheet (*.mcd)

But it would be unfair to others reading the forum to start having conversations about files they can't read! Not everyone will have access to Mathcad.

 

[builder_user]

Yup. File --> Save as --> Mathcad 2000 Worksheet (*.mcd)

But it would be unfair to others reading the forum to start having conversations about files they can't read! Not everyone will have access to Mathcad.

I didn't find another place to write result there 'cause it rather big

 

[gneill]

I looked at your Mathcad file. I thought that all the L's depended on K1, but you've specified L3 = 76*L0/K2.

You might try using a "symplify" operator (SmartMath symbolic keyword toolbar) to get a more compact result.

edit: Also make sure that all your i constants are really the square root of -1; it looks like some of the instances you have are just a variable i.

 

[builder_user]

result was not simpyfied

 

[builder_user]

How I need to make schelude for input resistance?

 

[gneill]

Unfortunately I don't know what a "schedule for input resistance" is. Perhaps there is another term in my local dialect.

Perhaps it has something to do with those mysterious K constants?

 

[builder_user]

K1=1.2
k2=0.7
k3=1.8

 

[gneill]

K1=1.2
k2=0.7
k3=1.8

Are these given values for the problem? It would have been nice to have them earlier, rather than having to carry the K's as variables through the algebra. Ah well.

 

[builder_user]

Are these given values for the problem? It would have been nice to have them earlier, rather than having to carry the K's as variables through the algebra. Ah well.

But they are not help 'cause the result is depend on w and i.And still rather big.

 

[gneill]

The "i" is just sqrt(-1). It tells you that the impedance is reactive in nature.

It's ω that's of interest. That is, "interesting" things happen when, for certain values of ω, the impedance of the circuit goes to zero or goes infinite. You should be able to solve for the values of ω where this happens. Maybe plot the impedance over a domain of frequencies that include them, and see how the impedance behaves.

 

[builder_user]

The "i" is just sqrt(-1). It tells you that the impedance is reactive in nature.

I know.

It's ω that's of interest. That is, "interesting" things happen when, for certain values of ω, the impedance of the circuit goes to zero or goes infinite. You should be able to solve for the values of ω where this happens. Maybe plot the impedance over a domain of frequencies that include them, and see how the impedance behaves.

I think I'll simplify it myself.And then solve this equatation for w

 

[builder_user]

Here the result

 

[gneill]

Here the result

The poles and zeroes appear to be in the right locations in your plot.

[For those who are reading who don't have Mathcad, I've attached an image of his impedance plot from the worksheet he's shared].