You\'re designing a speaker, and you want the tweeter to handle almost everythin

Question

You're designing a speaker, and you want the tweeter to handle almost everything above 1100 Hz, and woofer to handle almost everything below Hz.  The resistance of each speaker is 4 ohms.  In physics terms, these design parameters mean that for the RC ciruit connected to the tweeter, the impedance at 100 Hz should be 10x greater than the impedance at 1100 Hz.  For the RL circuit connected the woofer, the impedance at 1000 Hz should be 10x greater than the impedance at 100 Hz.. a.) Write down a formula for the impedance of the RC circuit as a function of the frequency  f (not w!).  b.) Write donw a formula for the impedance of the RL circuit as a function fo the frequency f (not w!).  c.) Find the capacitance that satisfies the design criteria.  d.) Find the inductance that satisfies the design criteria.

Explanation / Answer

a) RC circuit

impedance = R + XC

ZRC = R + 1/(2*pi*f*c)

b) RL circuit

impedance = R + XL

zRL = R + 2*pi*f*L

c)


accrding to given criteria,

ZRC(at 100 Hz) = 11*ZRC( at 1100 HZ)

R + 1/(2*pi*100*c) = 10*(R + 1/(2*pi*1100*c))


1/c*(1/2*pi*100 - 10/2*pi*1100) = 10*R - R

(1/c)*1.4476*10^-4 = 9*R

==>C = 1.4476*10^-4/(9*4) = 4.02*10^-6 F

d)
accrding to given criteria,

ZRL(at 1000 Hz) = 10*ZRL( at 100 HZ)

R + (2*pi*1000*L) = 10*(R + (2*pi*100*L))


L = 0

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