229-A1.2

• Activity: Passive Matching Networks
• Instructions: Each activity is structured as a tutorial, and you are expected to download the netlists, run the simulation, and make sure you understand the concepts and ideas presented. Should you have any questions, clarifications, or issues, please contact your instructor as soon as possible.
  • If you are new to ngspice, please visit the ngspice Tutorial page.
• At the end of this activity, the student should be able to:

1. Design and verify the performance of passive impedance matching circuits using ngspice.

Case 1: $R_{S}>R_{L}$

Let's design a single L-section circuit between a $5\mathrm {GHz}$ voltage source with output resistance, $R_{S}=50\mathrm {\Omega }$ and an amplifier with input resistance, $R_{L}=25\mathrm {\Omega }$.

• Calculate the matching factor, $m$,and the quality factor, $Q$.

$m={\frac {R_{S}}{R_{L}}}={\frac {50\mathrm {\Omega } }{25\mathrm {\Omega } }}=2$

(1)

$Q={\sqrt {m-1}}=1={\frac {R_{S}}{X_{1}}}={\frac {X_{1}^{\prime }}{R_{L}}}$

(2)

• Calculate the value of the reactance parallel to the larger resistance. In this case, the larger resistance is $R_{S}$.

$X_{1}={\frac {R_{S}}{Q}}={\frac {50}{1}}=50\mathrm {\Omega }$

(3)

• Calculate the second reactance, $X_{1}^{\prime }$, used to cancel $X_{1}$.

$X_{1}^{\prime }=R_{L}Q=25\mathrm {\Omega }$

(4)

• If we want a lowpass matching circuit, we need to use a capacitor for $X_{1}$, and an inductor for $X_{1}^{\prime }$. We can then calculate the capacitor and inductor values for $f_{0}=5\mathrm {GHz}$.

$C={\frac {1}{\omega X_{1}}}={\frac {1}{2\pi f_{0}X_{1}}}=636.52\mathrm {fF}$

(5)

$L={\frac {X_{1}^{\prime }}{\omega }}={\frac {X_{1}^{\prime }}{2\pi f_{0}}}=795.77\mathrm {pH}$

(6)

We can then create a SPICE netlist so we can verify the performance of our matching network. For circuits that you will reuse often, it is more often convenient to create a sub-circuit. In this case, a sub-circuit for our lowpass L-section:

1 .subckt l_match_lp hiR loR C=1p L=1n 
2 
3 C1		hiR y 	{C}
4 VC1		y 0	dc=0 ac=0
5 L1		loR x	{L}
6 VL1		x hir	dc=0 ac=0
7 
8 .ends l_match_lp

Note that the two voltage sources, VC1 and VL1, do not affect the circuit since they are set to zero volts. These dummy voltage sources are just there so we can measure the currents passing through the capacitor and inductor.