I am designing active inductor using OTAs (Transconductance amplifiers) and have a problem writing an equations.
I wrote two equations for nodes V2+ and V2- and input current Iin.
$$ 0=sCV^+_{2}+g_1(V^+_{1}-V^-_{1})$$
$$ 0=sCV^-_{2}-g_1(V^+_{1}-V^-_{1})$$
$$ I_o=g_2(V^+_{2}-V^-_{2})$$
If we express voltages from first and second equations, we get our new equations:
$$V^+_{2}=-\frac{g_1}{sC}(V^+_{1}-V^-_{1})$$
$$V^-_{2}=\frac{g_1}{sC}(V^+_{1}-V^-_{1})$$
So now if I put, my new equations into the third equation I get:
$$I_o=g_2(-\frac{g_1}{sC}(V^+_{1}-V^-_{1})-\frac{g_1}{sC}(V^+_{1}-V^-_{1}))$$
$$I_o=-\frac{2g_1g_2}{sC}(V^+_{1}-V^-_{1})$$
We also know that Io is equal to -Iin. After that we put above equation in equation for calculating the impedance:
$$Z=\frac{V^+_{1}-V^-_{1}}{I_{IN}}=\frac{V^+_{1}-V^-_{1}}{\frac{2g_1g_2}{sC}(V^+_{1}-V^-_{1})}=\frac{sC}{2g_1g_2}=sL$$
$$L=\frac{C}{2g_1g_2}$$
But when I try to simulate the circuit below, I get the inductance 4 times bigger and the equation should look like that:
$$L=\frac{2C}{g_1g_2}$$
Can somebody explain what am I doing wrong here?