R-parameters

Circuit description

Antoniou Gyrator grounded inductance simulating circuit using OVA and OTA are used in the design of multiple order High pass active filters in respect of their superiority in passing the signal from low frequency to extremely high frequency by using different configuration

For the purpose of calculating R parameters, we've added two ideal current generators to nodes 0-1 and 3-2.

Goals

• Solve the circuit with MNA
• Calculate Antoniou response $U$
• Calculate R parameters

Modeling the circuit

First we include Symbolics.jl and CircuitS.

using Symbolics
include("../CircuitS.jl")

Then we create the circuit and add all of the elements as shown in the picture above:

circuit = create_circuit()
add_element([Resistor, "R1", 4, 5], circuit)
add_element([Resistor, "R2", 3, 0], circuit)
add_element([Resistor, "R3", 1, 4], circuit)
add_element([Resistor, "R4", 5, 2], circuit)
add_element([Current, "Ig1", 0, 1], circuit)
add_element([Current, "Ig2", 3, 2], circuit)
add_element([OpAmp, "OpAmp1", [1, 5], 2], circuit)
add_element([OpAmp, "OpAmp2", [3, 5], 4], circuit)

Simulation

After we've built everything, we initialise and simulate the circuit:

init_circuit(circuit)
result = simulate(circuit)

println(result)

Dict{Any, Any} with 7 entries:
  "V5"       => -Ig2*R2
  "V3"       => -Ig2*R2
  "V2"       => (Ig1*R3*R4 - Ig2*R1*R2) / R1
  "I_OpAmp2" => (-Ig1*(-R1 - R3)) / R1
  "V4"       => -Ig2*R2 - Ig1*R3
  "I_OpAmp1" => (Ig2*R1 - Ig1*R3) / R1
  "V1"       => -Ig2*R2

Antoniou response is the voltage of node 3:

println(result["V3"])

-Ig2*R2

R parameters are defined as:

\[\begin{bmatrix} u_1\\ u_2 \end{bmatrix} = \begin{bmatrix} r_{11} & r_{12} \\ r_{21} & r_{22} \end{bmatrix} \begin{bmatrix} i_1\\ i_2 \end{bmatrix}\]

$i_1$ and $i_2$ are currents from our current sources, so all we have to do is calculate the voltage on those generators:

println(result["V1"])

println( simplify(result["V2"]-result["V3"], expand=true) )

-Ig2*R2
(Ig1*R3*R4) / R1

And in matrix form:

\[\begin{bmatrix} u_1\\ u_2 \end{bmatrix} = \begin{bmatrix} 0 & -R_2 \\ \frac{R_3R_4}{R_1} & 0 \end{bmatrix} \begin{bmatrix} i_1\\ i_2 \end{bmatrix}\]