开云体育

That's a very curious result that I didn't see coming.
Well worth figuring out.

Here's a python script to demonstrate what Roger says.
I chose L and C at random to be 1uH and 200pF.

Though I still don't fully understand it.


#############################################################
from math import pi, sqrt

L=1e-6; C=200e-12; # 1uH, 200pF
R = sqrt(L/C) # 70.71 ohms
rfreq=1/(2*pi*sqrt(L*C)) # expected resonant freq is 11.254mhz

for n in range(7):
freq = rfreq + (n-3)*1e6
ZL=2j*pi*freq*L
ZC= 1/(2j*pi*freq*C)
ZTOT = (ZL+R)*(ZC+R)/((ZL+R)+(ZC+R))
print ("mhz:", freq/1e6, "ZL:", ZL, "ZC:", ZC, "R:", R, "ZTOT:", ZTOT)
####################################################################

Prints the result below.
Note that all the ZTOT impedances are 70.71 ohms plus a wee bit of rounding error in the j part
The expected resonant frequency is the middle line, at 11.25 mhz.

mhz: 8.253953951963828 ZL: 51.86112219711599j ZC: -96.4113345059481j R: 70.71067811865476 ZTOT: (70.71067811865474+0j)
mhz: 9.253953951963828 ZL: 58.14430750429558j ZC: -85.99294091911938j R: 70.71067811865476 ZTOT: (70.71067811865476+3.0955136352074205e-15j)
mhz: 10.253953951963828 ZL: 64.42749281147518j ZC: -77.60662074234014j R: 70.71067811865476 ZTOT: (70.71067811865476+3.984830550267833e-15j)
mhz: 11.253953951963828 ZL: 70.71067811865476j ZC: -70.71067811865474j R: 70.71067811865476 ZTOT: (70.71067811865476-6.743286468322594e-16j)
mhz: 12.253953951963828 ZL: 76.99386342583433j ZC: -64.94024039742253j R: 70.71067811865476 ZTOT: (70.71067811865476+2.3942688709030205e-15j)
mhz: 13.253953951963828 ZL: 83.27704873301393j ZC: -60.0405523018712j R: 70.71067811865476 ZTOT: (70.71067811865474-1.5655109872331959e-15j)
mhz: 14.253953951963828 ZL: 89.5602340401935j ZC: -55.82834897188927j R: 70.71067811865476 ZTOT: (70.71067811865476+3.042457833625405e-15j)
"""


Jerry, KE7ER