L-Matching


The load impedance can be transformed up or down using matching network. Simplest matching network is L-match. The value of Q is determined by the ratio of R_{in} to R_{L}, and bandwidth is not controllable.
Upward transform : R_{in}>R_L
Downward transform : R_{in}<R_L



Lowpass Downward L-match

  • Downward transform the load impedance from R_{L} to R_{in}
  • Lowpass matching
  • Quality factor of the circuit, Q=\sqrt{\frac{R_{L}}{R_{in}}-1}
  • C_{1}=\frac{Q}{\omega_o R_{L}}
  • L_1={1\over \omega^2C_1}\left({Q^2 \over 1 + Q^2}\right)
  • Impedance Matching << Calculator >>

 

Highpass Downward L-match

  • Downward transform the load impedance from R_{L} to R_{in}
  • Highpass matching
  • Quality factor of the circuit, Q=\sqrt{\frac{R_{L}}{R_{in}}-1}
  • L_{1}=\frac{R_{L}}{\omega_o Q}
  • C_{1}=\frac{1}{\omega_o^2 L_{1}}\left(1+{1\over Q^2}\right)

 

Lowpass Upward L-match

  • Upward transform the load impedance from R_{L} to R_{in}
  • Lowpass matching
  • Quality factor of the circuit, Q=\sqrt{\frac{R_{in}}{R_{L}}-1}
  • L_{1}=\frac{Q R_{L}}{\omega_o}
  • C_{1}=\frac{1}{\omega_o^2 L_{1}}\left({Q^2 \over 1 + Q^2}\right)

 

Highpass Upward L-match

  • Upward transform the load impedance from R_{L} to R_{in}
  • highpass matching
  • Quality factor of the circuit, Q=\sqrt{\frac{R_{in}}{R_{L}}-1}
  • C_{1}=\frac{1}{\omega_o Q R_{L}}
  • L_{1}=\frac{1}{\omega_o^2 C_{1}}\left(1 +{1 \over Q^2}\right)

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