Patch antenna "series-shunt" feed array impedance matching

I'm trying to understand how is attached feedline matched. Thin lines are 100Ω transmission line. Matching structure looks somewhat similar to one shown here:



Z0 = sqrt(Zs*ZL), ZL = Z0^2/Zs

Going right to left, 100Ω source, through 70Ω quarter wavelength Z0, load is equal to 50Ω, or two 100Ω in parallel. Second patch, is same, except quarter wavelength is at Z0 = 80Ω, load equals 64Ω, or 100Ω parallel with 177Ω, meaning that impedance of 100Ω leftmost patch in series with quarter wavelength transformer, with Z0 = 60Ω and another quarter wavelength transformer with Z0 = 100Ω must equal to 177Ω. Using same method of analysis, I transform impedance of leftmost patch to ZL = 60^2/100 = 36Ω, and again (now, 36Ω being the source) to 100^2/36 = 277Ω != 177Ω. Not sure what did wrong it's a simple transformation. Also, I know that these are correct impedance value as antenna with this feed method is build and works quite well.

Are you sure that patch input impedance is 100 Ohm? Thin 100 ohm lines may act as quarterwave transformers to some higher impedance (if length to patch is 90deg). Also thin 100 ohm line may act as impedance repeater (if length to patch is 180deg), and repeat some virtual high impedance from T-junction center to the patch. Are you sure that 60 ohm line and 100 ohm line near left patch are both quarterwave?
I did some calculations on your array
It seems that it uses weighting 0.5+0.315+0.185=1 (right,left,center patch). Patch input impedance may be 170 Ohm, but it depends on feeding line length, you need to clarify sizes and we will continue to investigate. You can put my calculations to speqmath freeware program and try some values.

Georgy.Moshkin said:

Are you sure that patch input impedance is 100 Ohm? Thin 100 ohm lines may act as quarterwave transformers to some higher impedance (if length to patch is 90deg). Also thin 100 ohm line may act as impedance repeater (if length to patch is 180deg), and repeat some virtual high impedance from T-junction center to the patch. Are you sure that 60 ohm line and 100 ohm line near left patch are both quarterwave?
I did some calculations on your array
It seems that it uses weighting 0.5+0.315+0.185=1 (right,left,center patch). Patch input impedance may be 170 Ohm, but it depends on feeding line length, you need to clarify sizes and we will continue to investigate. You can put my calculations to speqmath freeware program and try some values.

Code:

z1=100; ' patch input impedance
zx=100; ' common line impedane

'  right patch
p=1
	p = 1.000000000

z0=z1*p/(1+p)
	z0 = 50.000000000
z2=z0*(1+p)
	z2 = 100.000000000
Sqrt(zx*z0)
	Ans = 70.710678119
Sqrt(zx*z2)
	Ans = 100.000000000

Sqrt(zx*z0)
	Ans = 70.710678119
Sqrt(zx*z2) ' do not need to be transformed 100=100
	Ans = 100.000000000


' center patch
p=1.8
	p = 1.800000000

z0=z1*p/(1+p)
	z0 = 64.285714286
z2=z0*(1+p) '
	z2 = 180.000000000

Sqrt(zx*z0) ' 80 Ohm line
	Ans = 80.178372574
Sqrt(170*60) ' 100 ohm quarterwave line
	Ans = 100.995049384

' 60 ohm line maybe not quarterwave transformer

' left patch (patch input impedance may be 170 ohm)
Sqrt(60*170)
	Ans = 100.995049384



' right patch
p=0.5 ' to patch
	p = 0.500000000

(1-p) ' to next patch
	Ans = 0.500000000

p=p/(1-p) ' ratio
	p = 1.000000000

' center patch
p=0.63 ' to patch
	p = 0.630000000

(1-p) ' to next patch
	Ans = 0.370000000

p=p/(1-p) ' ratio
	p = 1.702702703

0.5*0.63
	Ans = 0.315000000
0.5*0.37
	Ans = 0.185000000

' weighting right-center-left:
0.5+0.315+0.185
	Ans = 1.000000000

Click to expand...

Yes, I measured output impedance out of leftmost patch and measured 177Ω, thank you.

And other two patches have 100 ohm input impedance?
Soleftmost patch is a matching-type patch? I have seen some paper where last patch was different, and called "matching element", but it is pretty rare.
In such arrays patches are usually identical to each other.