Calculate Resistance from Z and Phase? - diyAudio
 Calculate Resistance from Z and Phase?
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 8th December 2013, 06:02 PM #1 diyAudio Member     Join Date: Jun 2009 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 06:17 PM.
 8th December 2013, 06:19 PM #2 diyAudio Member   Join Date: Nov 2003 Location: Brighton UK Hi, At 30 degrees the real part is (cos) 0.866xZ R, imaginary is (sin) 0.5xZ. rgds, sreten. __________________ There is nothing more practical than a really good theory - Ludwig Boltzmann When your only tool is a hammer, every problem looks like a nail - Abraham Maslow
 8th December 2013, 06:42 PM #3 diyAudio Member     Join Date: Jun 2009 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 06:55 PM.
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Quote:
 Originally Posted by kouiky 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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