The circuit shown below is a model of the electrostatic spea

The circuit shown below is a model of the electrostatic speakers constructed by several UAA EE students. Two important speaker characteristics are 1) the input impedance as seen by the amplifier, and 2) the frequency response of the speaker. Determine the is the input impedance as seen by the amplifier, which includes the two drivers, as well as the high and low-pass filters. You will need to measure this as a function of frequency and plot both its amplitude and phase for the frequency range f = 20 - 20kHz. A circuit model for the speaker is given below with C_p = 11 mu F corresponding to the electrostatic panel and with R_5 = 3.2 Ohm and L_3 = 1.7mH modeling the low frequency driver (woofer). Element values are given by, R_1 = 2.7 Ohm R_2 = 3.5 Ohm C_1 = 80 mu F C_p = 11 mu F L_1 = 2 mH R_3 = .28 Ohm R_4 = 1 Ohm R_5 = 3.2 Ohm C_2 = 250 mu F L_2 = 1.5 mH L_3 = 1.7 mH Derive and plot two transfer functions, one with the output being the voltage across the electro-static panel (corresponding to the voltage across the capacitor C_p), and the second corresponding to the voltage across the woofer (corresponding to the voltage across the series combination of R_5 and L_3). Each transfer function should be plotted in terms of its amplitude and phase over the frequency range 20 - 20kHz.

Solution

1. input resistance = 2.7 + 1/jwC

= 2.7 + j35

amplitude = 3.5 + jw*.002 /1/jwc

= a+ib