Back-To-Back VCIS

The circuit is an impedance converter using a back-to-back voltage-controlled current sources (VCIS). This specific circuit uses only a resistor at port 2. Input Impedance: Iin = -Gm2 · V2 Iin = -Gm2 [-(Gm1 · V1)(Z2)] Iin = Gm1 · Gm2 · Z2 · V1 Iin = Gm1 · Gm2 · Z2 · Vin Zin = Vin/Iin Zin = 1 / (Gm1 · Gm2 · Z2) Zin = [1 / (Gm1 · Gm2)] · (1 / Z2) The driving circuit at port 1 sees a scaled reciprocal of the impedance at port 2. The scaling factor is the reciprocal of the product of the transconductances of the two VCISs. For the saved values, Zin = 1 / [(25 mA/V)(4 mA/V)(200 Ω)] Zin = 1 / (20,000 µA·Ω/V²) Zin = 1 / (20 mA/V) = 1 / (0.02 A/V) Zin = 50 Ω The resistance of 200 Ω at port 2 is seen as a 50 Ω resistance at port 1, this causes a 20 mA current for a 1 V input voltage. The reciprocal of resistance is conductance, the scaling factor [1 / (Gm1 · Gm2)] converts the conductance back to resistance. Voltage Gain: Vout = -(Gm1 · Vin)(R) Vout = -(25 mA/V · Vin)(200 Ω) Vout = -5 · Vin Av = Vout/Vin = -5 For the saved input of 1 V, the voltage developed at port 2 is -5 V. The voltage gain can be made positive by reversing the output current directions of the two VCISs. This will not affect the input impedance.