Re: S11 inductance measurement

Thanks, Tony. Your tinyurl link works fine. It displays the gyrator circuit.

My link was produced by Falstad's version 1.5n which is no longer up-to-date with the website version. I suspected it would misbehave. I use the older version because it allows me to rearrange scope traces by editing the file directly in the Export window.

I must confess I've never computed L from s11.

From your datasheet. 50 Ohms @ 100MHz has s11 =0.333, 30 degrees which is a VSWR of 2.0 and return loss of 9.6 dB

Z = Zo * ((1 + Γ) / (1 - Γ))
Γ = (Z - Zo) / (Z + Zo)
S11 = 20 * Log10(mag)

Reflected power is the square of reflection coefficient or 1/9th or 11.1% in this example.



same example
Z= 82.9Ω +j30.7Ω

L=Z_Im/2πf
L= 30.7/(2π*1e8Hz) = 49 nH

have fun.

Why do "denominator addition" and "numerator addition" ?

Do you guys have any idea how the author arrived at this expression exactly ?

Surely learn and study very basic things.

Z=(1+S.11)/(1-S.11)

Z_numerator=1+S.11=(1+S.11_re) + j*S.11_im
Z_denominator=1-S.11=(1-S.11_re) + j*(-S.11_im)

Z_numerator_re=1+S.11_re
Z_numerator_im=S.11_im

Z_denominator_re=1-S.11_re
Z_denominator_im=-S.11_im

Could anyone tell me why I am not getting Leq to be 1nH ?

* gnetlist -g spice-noqsi -o test_active_inductor.net test_active_inductor.sch
* SPICE file generated by spice-noqsi version 20130710
* Send requests or bug reports to jpd@noqsi.com
RZ1 Vtest Ltest 50      
Vtest Vtest GND dc 1
+ac 1
.GLOBAL Vdd Vss
.PARAM SUPPLY=3.3v
.options TEMP=25
.MODEL n1 NMOS
.MODEL p1 PMOS
.INCLUDE CMOS_Inverter.net
.INCLUDE Gm2.net
Vd Vdd GND 'SUPPLY'
Vs Vss GND 0V
Ltest Ltest GND 1n  
.control
set noaskquit
AC LIN 1000 100Meg 200Meg
run
let S11=(2*v(Ltest)/v(Vtest)-1)
settype s-param S11

let S11db=db(S11)
settype decibel S11db

let P11=180*ph(s11)/pi
settype phase P11

plot s11db ylimit -0.5 0
plot P11

print S11 > S11.log
*plot smithgrid S11
*wrs2p s3046.s2p S write touchstone vers. 1 file s3046.s2p
.endc

Found the root cause for the miscalculation.

I forgot to multiply by Zo which is 50ohm

You can still do that with this version
http://tinyurl.com/y946spno
http://tinyurl.com/y72hdnj6 without current trace