A low-pass RC section ( ,

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Circuit foundations and passive networks · Signals, systems, control and digital signal processing

Electronics for Measurement, Ch Phasors, impedance and the frequency response

Problem

A low-pass RC section (R1=4.7 kΩR_1 = 4.7\,\mathrm{k}\Omega, C1=1.8 nFC_1 = 1.8\,\mathrm{nF}, corner fA=18.8 kHzf_A = 18.8\,\mathrm{kHz}) is directly cascaded (no buffering) into a high-pass RC section (R2=4.7 kΩR_2 = 4.7\,\mathrm{k}\Omega, C2=180 nFC_2 = 180\,\mathrm{nF}, corner fB=188 Hzf_B = 188\,\mathrm{Hz}). Someone argues: "the low-pass alone has HA(jf)=1/(1+jf/fA)H_A(jf) = 1/(1+jf/f_A) and the high-pass alone has HB(jf)=(jf/fB)/(1+jf/fB)H_B(jf) = (jf/f_B)/(1+jf/f_B); at f=2.0 kHzf = 2.0\,\mathrm{kHz}, well below fAf_A and well above fBf_B, each section alone is close to its passband value of 11, so the cascade's overall gain there is 1×1=11\times1 = 1, i.e. 0 dB0\,\mathrm{dB}." ((a)) Find the error in this reasoning. ((b)) Estimate the true mid-band gain (in decibels) at 2.0 kHz2.0\,\mathrm{kHz}, using the fact that the resistor values are equal.

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