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### Network # LCR Measurements

J

#### [email protected]

Jan 1, 1970
0
Hello,

I have a question that I hope somebody can help me with. I have a LCR
meter and I am sweeping some components. I am recording |Z| and the
phase angle. How can I calculate the R, L, and C at each of the
different frequencies I have recorded.

Thanks,
jp

J

Jan 1, 1970
0
I have a question that I hope somebody can help me with. I have a LCR
meter and I am sweeping some components. I am recording |Z| and the
phase angle. How can I calculate the R, L, and C at each of the
different frequencies I have recorded.

Mmm... are you sure this isn't a homework question?

Take the measurement you have (magnitude and angle) and express it in
rectangular coordinates, Z=R+jX. R is the resistance, and then knowing that
X=2*pi*L or -1/(2*pi*C), you can solve for C. (If X is positive, you have an
inductor, otherwise it's a capacitor, of course.)

J

#### [email protected]

Jan 1, 1970
0
Mmm... are you sure this isn't a homework question?

Take the measurement you have (magnitude and angle) and express it in
rectangular coordinates, Z=R+jX. R is the resistance, and then knowing that
X=2*pi*L or -1/(2*pi*C), you can solve for C. (If X is positive, you have an
inductor, otherwise it's a capacitor, of course.)

No.... it's not a homework question. jX will indicate if the circuit
is capacitive or inductive. However, I have a series RLC circuit and
would like to calculate the R,L, and C from the lcr data. The part I'm
having a problem with is extracting the L and C values individually.

J

Jan 1, 1970
0
No.... it's not a homework question. jX will indicate if the circuit
is capacitive or inductive. However, I have a series RLC circuit and
would like to calculate the R,L, and C from the lcr data. The part I'm
having a problem with is extracting the L and C values individually.

Ah, OK. This is impossible to do if you measure the impedance at only one
frequency (since you have three unknowns -- R, L, and C -- but only two
equations, Re(Z) and Im(Z) ). What you do instead is:

1) Measure the impedance at two (or more) frequencies, set up a system of
equations and solve (use, e.g., least-squares fitting if you use more than two
equations). Most LCR meters will let you choose at least two different test
frequencies.
2) (The way people usually do this...) Use an adjustable frequency generator,
connect your circuit to its output, and sweep the frequency until you maximize
the current through the circuit (this corresponds to the minimum |Z|). The
idea here is that a current maximum is reached at resonance, at which point
f*L=1/(f*C), and now that you have enough information to solve for all the
unknowns.
3) (Seemed to be a popular lab exercise in school...) Similar to #2, you find
the 3dB points of the impedances response as well as the resonant frequency,
then you compute Q, and since you can reasure the resistance directly from Q
and R you can compute L or C from Q~=2pi*fL/R or Q~=1/(2pi*fC*R). I believe
the idea is that this approach tends to be a little more accurate than (2)
since by measuring both 3dB points you're doing a bit of averaging and are
somewhat out from resonances where, if you have a high-Q circuit, measurement
accuracy is often compromised.

If you're lucky enough to have access to a network analyzer, you just tell it
to measure S_{11} over some frequency range and it'll then find the minimum
|Z| for you and read out the R, L, and C directly at that point. The
network analyzer approach is also useful to give you some idea of how accurate
a simple series RLC model is for your particular circuit.

---Joel

J

#### [email protected]

Jan 1, 1970
0
Ah, OK. This is impossible to do if you measure the impedance at only one
frequency (since you have three unknowns -- R, L, and C -- but only two
equations, Re(Z) and Im(Z) ). What you do instead is:

1) Measure the impedance at two (or more) frequencies, set up a system of
equations and solve (use, e.g., least-squares fitting if you use more than two
equations). Most LCR meters will let you choose at least two different test
frequencies.
2) (The way people usually do this...) Use an adjustable frequency generator,
connect your circuit to its output, and sweep the frequency until you maximize
the current through the circuit (this corresponds to the minimum |Z|). The
idea here is that a current maximum is reached at resonance, at which point
f*L=1/(f*C), and now that you have enough information to solve for all the
unknowns.
3) (Seemed to be a popular lab exercise in school...) Similar to #2, you find
the 3dB points of the impedances response as well as the resonant frequency,
then you compute Q, and since you can reasure the resistance directly from Q
and R you can compute L or C from Q~=2pi*fL/R or Q~=1/(2pi*fC*R). I believe
the idea is that this approach tends to be a little more accurate than (2)
since by measuring both 3dB points you're doing a bit of averaging and are
somewhat out from resonances where, if you have a high-Q circuit, measurement
accuracy is often compromised.

If you're lucky enough to have access to a network analyzer, you just tell it
to measure S_{11} over some frequency range and it'll then find the minimum
|Z| for you and read out the R, L, and C directly at that point. The
network analyzer approach is also useful to give you some idea of how accurate
a simple series RLC model is for your particular circuit.

---Joel

Thanks for your help!

D

#### [email protected]

Jan 1, 1970
0
Hello,

I have a question that I hope somebody can help me with. I have a LCR
meter and I am sweeping some components. I am recording |Z| and the
phase angle. How can I calculate the R, L, and C at each of the
different frequencies I have recorded.

Thanks,
jp

I am not expert
but if measures the answer to an impulse
you do not succeed to go back to the transfer function
and to calculate poles and zero then
and knowing the structure of the net
to go back to the values?
aspect answers from who is more expert than me

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