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kuroda

Apply Kuroda's transformation based on Kuroda's identities

    Description

    example

    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

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    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

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

    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.

    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.

    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

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    Circuit element, returned as a circuit object.

    Algorithms

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    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].

    Kuroda's Transformation: Shunt capacitor to series inductor, series inductor to shunt capacitor, series capacitor to N:1 transformer, and shunt inductor to 1:n transformer.

    References

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

    Introduced in R2021b