Hi guys,
I was away this past weekend and see nothing has changed much.
Anyway to get back to my modeling analysis:
Looking at Steve's proposal based on the magnitude of the impedances, I was wrong in that the importance of Inductance is artifically inflated.
(BTW - I think some of Steve's constants are also wrong)
So Lets take an indepth look at Steve's equation.
R = R
Inductive impedance = 2*pi*f*L (where L=henry's)
Capacitive impedance = 1/(2*pi*f*C) (where C=farads)
At 20 Hz, 2*pi*f = 125.6636
At 20k Hz, 2*pi*f = 125663.7
Clarity 7 measured parameters
R (100 Hz) = 0.00324 Ohms
R (20k Hz) = 0.003399 Ohms
L (100 Hz) = 0.049 x 10<sup>-6</sup> Henry's
L (20k Hz) = 0.058 x 10<sup>-6</sup> Henry's
C (100 Hz) = 98 x 10<sup>-12</sup> Farads
C (20k Hz) = 97.2 x 10<sup>-12</sup> Farads
Steve proposed 20 Hz, but since Gene did not measure at 20 Hz but 100 Hz, we'll probably be safe using the 100 Hz numbers and calling them 20 Hz numbers. Even if we changed f to 100, the results below would change in number only, not relative to each other.
HF (& LF) = (R*0.5) + (L*2*pi*f*0.35)+((1/C*2*pi*f)*0.15
20 Hz Merit = (R*0.5) + L*125.6637*0.35) + (0.15/(C*125.6637)
20 Hz Merit = (R*0.5) + L*43.982) + (1.194 x 10<sup>-3</sup>/(C)
20 Hz Merit = 0.0017 + 2.155 x 10<sup>-6</sup> + 12180225.8
20 Hz Merit = 12180225.8
20k Hz Merit = (R*0.5) + L*125663.7*0.35) + (0.15/(C*125663.7)
20k Hz Merit = (R*0.5) + L*43982) + (1.194 x 10<sup>-6</sup>/(C)
20k Hz Merit = 0.0016995 + 7.2885 x 10<sup>-3</sup> + 12280.47
20k Hz Merit = 12280.47
Since it's casual to the most obvious observer that capacitance is the only thing that matters in Steve's equation I stand corrected. But maybe I'm missing something so obvious I can't see the forest through the trees.
BTW - I think I'll stay with my dimensionless model, which BTW uses similar weighting factors to the ones Steve proposes (i.e. 50% for R, 35% for L, and 15% for C). Which to answer John's question too, were arrived at by yanking numbers out of my butt. Really they were, but then I also asked Gene about it for verification.
My new question asks, how is the RLC circuit modeled?
Are all elements (real and imaginative) in series, are L and R in series and parallel to C, are all three parallel to each other? Because 1/(2*pi*f*C) is a really big number when C is picofarads (10<sup>-12</sup> Farads).
And for a really big finale, do harmonics really affect the impedance to the degree emphasized by modding the equations, I'm thinking of 2*pi*f*n*L or 1/2*pi*f*n*C?