kuroda

Apply Kuroda's transformation based on Kuroda's identities

Syntax

outObj = kuroda(inObj,EL1,EL2)

outObj = kuroda(inObj,EL1,EL2,EL3)

Description

outObj = kuroda(inObj,EL1,EL2) applies the suitable Kuroda's identity to the two elements EL1 and EL2 in the circuit inObj.

outObj = kuroda(inObj,EL1,EL2,EL3) applies the suitable Kuroda's identity to the of three elements EL1, EL2, and EL3.

Note

You can apply Kuroda's identities only to circuits where all negative terminals of the ports share the same node.

Examples

Apply Kuroda's Transformation to Two Elements

Create a lowpass pi LC ladder object.

L = 3.18e-8;
C = [6.37e-12 6.37e-12];
lpp = lcladder('lowpasspi',L,C);

Apply Richards' transformation to the LC ladder object.

r = richards(lpp,1e9)

r = 
  circuit: Circuit element

    ElementNames: {'C_tx'  'L_tx'  'C_1_tx'}
        Elements: [1x3 txlineElectricalLength]
           Nodes: [0 1 2 3 4]
            Name: 'unnamed'
        NumPorts: 2
       Terminals: {'p1+'  'p2+'  'p1-'  'p2-'}

Insert a unit element at port 1 of the circuit at the operating frequency of 1 GHz and characteristic impedance of 50 ohms.

UE = insertUnitElement(r,'C_tx',1,1e9,50)

UE = 
  circuit: Circuit element

    ElementNames: {'C_tx_p1_elem_UE'  'C_tx'  'L_tx'  'C_1_tx'}
        Elements: [1x4 txlineElectricalLength]
           Nodes: [0 1 2 3 4 5]
            Name: 'unnamed'
        NumPorts: 2
       Terminals: {'p1+'  'p2+'  'p1-'  'p2-'}

Apply Kuroda's transformation to the two elements C_tx_p1_elem_UE and C_tx.

ku = kuroda(UE,'C_tx_p1_elem_UE','C_tx')

ku = 
  circuit: Circuit element

    ElementNames: {1x4 cell}
        Elements: [1x4 txlineElectricalLength]
           Nodes: [0 1 2 3 4 5]
            Name: 'unnamed'
        NumPorts: 2
       Terminals: {'p1+'  'p2+'  'p1-'  'p2-'}

Input Arguments

inObj — RF circuit

circuit object

RF circuit, specified as a circuit object. The circuit object can have a txlineElectricalLength object as one of its elements.

EL1 — First element

txlineElectricalLength object | scalar

First element in inObj, specified as a txlineElectricalLength object or a scalar. When you specify the value as scalar, the value refers to an index of element in the circuit. This element must be sequentially connected to the second element specified in the Kuroda's transformation.

EL2 — Second Element

txlineElectricalLength object | scalar

Second element in inObj, specified as a txlineElectricalLength object or a scalar. When you specify the value as scalar, the value refers to an index of element in the circuit. This element must be sequentially connected to the first element specified in the Kuroda's transformation.

EL3 — Third element

nport object | scalar

Third element in inObj, specified as an nport object or a scalar. When you specify the value as an nport object the value refers to an ideal transformer and when you specify the value as a scalar, the value refers to an index of element in the circuit.

An ideal transformer is implemented by using a 2-port nport element with S-parameter data corresponding to an 1:N or N:1 ideal transformer. That is, the transformer must be passive, lossless, frequency independent, and with S-parameter data conforming to S12 = S21, and S12 = N x (1+S11), where N is the number of turns in a transformer.

This element must be sequentially connected to the first two elements specified in the Kuroda's transformation.

Output Arguments

outObj — Circuit element

circuit object

Circuit element, returned as a circuit object.

Algorithms

Kuroda's Transformation

This figure shows how you can apply Kuroda's transformation or identities to a shunt capacitor, shunt inductor, series capacitor,or series inductor [1].

References

[1] Pozar, David M. Microwave Engineering. 4th ed. Hoboken, NJ: Wiley, 2012.

Version History

Introduced in R2021b