Signals and Networks: Negative impedance converter

Negative impedance converter

The negative impedance converter (NIC) is a one-port op-amp circuit acting as a negative load which injects energy into circuits. This reverses the voltage polarity or the current direction of the port and introduces a phase shift of 180° (inversion) between the voltage and the current for any signal generator.

(Negative impedance converter)

The op-amp output voltage is

V_{\text{opamp}} = V_s \left( 1 + \frac{R_2}{R_1} \right)\,

The current going from the operational amplifier output through resistor

R_3

toward the source

V_s

is

-I_s

, and

-I_s = \frac{ V_{\text{opamp}} - V_s }{ R_3 } = V_s \frac{ \frac{R_2}{R_1} }{ R_3 }.

So the input

V_s

experiences an opposing current

-I_s

that is proportional to

V_s

, and the circuit acts like a resistor with negative resistance

R_{\text{in}} \triangleq \frac{V_s}{I_s} = -R_3 \frac{R_1}{R_2}.

Negative capacitance circuit

Z_\text{in} = {v \over i} = {j \over {\omega C}}

Negative inductance circuit

Z_\text{in} = {v \over i} = -j \omega C R_1^2