Confusing gamma_in in microstrip whose Z0^2 equals Zin*Zl

[jimway]

I was totally confused

i was totally confused. When using a microstripe whose Z0^2 equals Zin*Zl and length is quarter of the wave legnth to match the Zin and Zl, the gamma_in should be zero. But gamma_in equals (Zin-Z0)/(Zin +Z0), while gamma_in won't be zero.
e.g. Zin=50 Zout=75 then Z0 should be 61.24 while gamma_in equals (75-61.24)/(75+61.24)

 

[gecky]

Re: I was totally confused

Hi

you are talking about a quarter-wave transformer.

what u cal : Zi^2 = Z0*Zrequired. Here Zi is the impedence of the TL u must use for the transformer to do impedence matching. U then go ahead and insert 1/4 wavelength (at the operating freq) of this TL .

Look up any text that teaches smith-chart, they'll explain it better.

 

[jimway]

Re: I was totally confused

But shouldn't it be normalized by the characteristic impedance of th TL?

 

[wky]

Re: I was totally confused

When under matched condition, Zin will see an impedance equal to Zin itself (that is the meaning of matching). Hence the gamma is zero.

 

[jimway]

Re: I was totally confused

The gamma_in equals (Zin-Z0)/(Zin +Z0), while gamma_in won't be zero in this situation

 

[molloy]

Re: I was totally confused

Dont be confused: the Z0 in the expression of gamma_in is the load impedance, in the other case is the characteristic impedance

 

[dhlee]

Re: I was totally confused

In your example, the Z0(61.24ohm) is the characteristic impedance of quarterwave transformer, so when you calculate the input reflection coefficient, you should take the Z0 as a 50ohm(source impedance).
As you say, the Zin=50 and the source impedance Z0 is 50ohm so the Gamma_in is zero.

 

[wky]

Re: I was totally confused

The gamma_in equals (Zin-Z0)/(Zin +Z0), while gamma_in won't be zero in this situation

When a source with source impedance Z1 feeds a load Z2, the gamma is
(Z1-Z2)/(Z1+Z2).

In your case, Z1=Zin=50 and Z2=50 (as the load ZL which is 75 is now reflected as 50 ohm at the source end). Therefore gamma is 0.