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Old 8th December 2013, 05:02 PM   #1
kouiky is offline kouiky  United States
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Default Calculate Resistance from Z and Phase?

My mind must be slipping today. If I have a known impedance with a known phase shift, what is the equation to calculate the parallel capacitance and find the resistance without that phase shift?

Example: 6 Ohms impedance, -30 degrees. I need to find that capacitance value and remove that to then find the resistance at zero shift.

Last edited by kouiky; 8th December 2013 at 05:17 PM.
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Old 8th December 2013, 05:19 PM   #2
sreten is offline sreten  United Kingdom
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Hi,

At 30 degrees the real part is (cos) 0.866xZ R, imaginary is (sin) 0.5xZ.

rgds, sreten.
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Old 8th December 2013, 05:42 PM   #3
kouiky is offline kouiky  United States
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Does this work for calculating the resistance component of a speaker driver when the Z and phase are known?

Last edited by kouiky; 8th December 2013 at 05:55 PM.
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Old 8th December 2013, 08:01 PM   #4
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Quote:
Originally Posted by kouiky View Post
My mind must be slipping today. If I have a known impedance with a known phase shift, what is the equation to calculate the parallel capacitance and find the resistance without that phase shift?

Example: 6 Ohms impedance, -30 degrees. I need to find that capacitance value and remove that to then find the resistance at zero shift.
Do you mean that you want to know the equivalent parallel resistance and equivalent parallel capacitance?

mag(Y)=1/mag(Z)

phi(Y)=-phi(Z)

G=mag(Y)*cos(phi(Y))

Rparallel=1/G

B=mag(Y)*sin(phi(Y))

Cparallel=B/(2*pi*f)

Hence, using cos(-x)=cos(x) and sin(-x)=-sin(x):

Rparallel=mag(Z)/cos(phi(Z))

Cparallel=-sin(phi(Z))/(mag(Z)*2*pi*f)

With mag(Z)=6 ohm, phi(Z)=-30 degrees:

Rparallel~=6.92820323 ohm

Cparallel unknown because the frequency is not specified. Examples:

f=1 Hz -> Cparallel~=13262.91192 uF
f=1 kHz -> Cparallel~=13.26291192 uF
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