Q factor of match circuit for complex impedance

[Young_Electronic_00]

Hello,

I've short question related to Q factor of PI match circuit. I'm quite confused, because in every pdf and book I see matching between resistances. The equation for such case is: Q = sqrt((Rout/Rin)-1). What if i calculate this parameter for Rin=50ohms and Rout = 100+i43 ohms? Should i firstly calculate module for Rout?

Regards,
E.

 

[FvM]

The calculated value according to your equation is the minimal Q achievable by a matching network. The respective network is a L network. A pi or T-network has generally higher Q.

For those cases where the reactive load component can be absorbed by the L network, you can convert the series impedance circuit 100 + j43 to a parallel circuit 118.5 || j 275.5 and obtain the minimal Q for the parallel R value. It's probably simpler to use a matching network calculator like Impedance Matching Network Designer (sandiego.edu)

 

[Young_Electronic_00]

FvM Thank you for reply. I sometimes use this website Well, I know that for pi and T topologies Q factor can be quite big. I just want to check how complex output impedance change the Q factor so this is the reason why I ask for that. Moreover, i was wondering how to calculate case where Zout is 50 ohms and Zin is 54 ohms. According to cited equation The Q factor will be smaller than 1... as i know such A value has no sense.

 

[FvM]

I just want to check how complex output impedance change the Q factor

I showed how you find the answer for this particular case. Q = sqrt(118.5/50 -1) = 1.17

Moreover, i was wondering how to calculate case where Zout is 50 ohms and Zin is 54 ohms. According to cited equation The Q factor will be smaller than 1... as i know such A value has no sense.

Just a problem of using the equation beyond it's range of validity. Calculate 54/50 instead of 50/54.

 

[Young_Electronic_00]

Ok... but if I calculate Q factor for the case 54/50 I'll still have value smaller than unity, right? I mean Q= sqrt((54/50) -1) is about 0.28. I'm wrong? By the way please confirm that I undersand it in proper way - this equation is related only with L network ?

 

[FvM]

0.28 sounds reasonable. Q of an ideal wide band matching, e.g by transformer is 0, Q = 1 involves limited bandwidth.