For the following circuit the middle band gain is:
\$A_v=-g_mR_D\cdot R_{in}/(R_{in}+R_{sig})\$, where \$R_{in}=47\cdot 10/57=8.25M\Omega\$ and \$R_D=4.7 || 10k\$
The total resistance which the capacitor 0.1uF "sees" is \$10k+4.7k=14.7k\$
The total resistance which the capacitor 10uF "sees" is \$R_S || 1/g_m\$
The total resistance which the capacitor 0.01uF "sees" is \$100k+8.25M=8.35M\$
Hence,
\$f_{p3}=1/(2\pi\cdot 14.7k\cdot 0.1\mu F)\$
\$f_{p2}=1/(2\pi\cdot R_S || 1/g_m\cdot 10\mu F)\$
\$f_{p1}=1/(2\pi\cdot 8.35M\cdot 0.01\mu F)\$
\$f_{L}=f_{p1}+f_{p2}+f_{p3}\$
I then found \$A(s)=-((8.25M+1/sC_1)/(8.35M+1/sC_1)) \cdot g_m((10k+1/sC_3)||4.7k)/(1+g_m(2k||1/sC2))\$
This yielded for the zeros:
\$f_{z1}=1/(2 \pi \cdot 8.25M \cdot C_1)\$
\$f_{z2}=1/(2 \pi \cdot 2k \cdot C_2)\$
\$f_{z3}=1/(2 \pi \cdot 10k \cdot C_3)\$
Hence, \$f_{p3}<f_{z3}, f_{p1}<f_{z1}\$ whereas I was asked to prove that in this circuit for each capacitor \$f_{zi}<f_{pi}\$.
What was I doing wrong? Could anyone please help settling this discrepancy?
