On Sun, Dec 22, 2019 at 11:32 AM, <erik@...> wrote:
In /g/nanovna-users/message/8494 they provide the proof they
are mathematically the same.
The GIN&PEZ equation certainly seems to give the same result as the standard one-port 3-term correction equations. Here's a quick Matlab example I wrote, using the GIN&PEZ terminology and values pulled out of the air for short, open, load, and measured DUT gamma:
MATLAB CODE
S = -0.9; % Actual Gamma of Short
O = 0.9; % Actual Gamma of Open
L = 0.1+1i*0.1; % Actual Gamma of Load
s = -0.8+1i*0.1; % measured Gamma of Short
o = 0.85-1i*0.15; % measured Gamma of Open
l = 0.2; % measured Gamma of Load
g = 0.5+1i*0.5 % measured Gamma of DUT
% G will be the actual (calculated) Gamma of the DUT.
% First, Gamma calculated according to GIN&PEZ
Gginpez = (S*(L-O)*(g*s+l*o)+L*(O-S)*(g*l+o*s)+O*(S-L)*(g*o+s*l))/...
((L-O)*(g*s+l*o)+ (O-S)*(g*l+o*s) + (S-L)*(g*o+s*l))
% Now, Gamma calculated per 3-term one-port correction formulas:
% (see equations 1, 5, 6, and 7 in the User Guide down-loadable from:
% )
% First, four preliminary equations...
D = S*(O-L)*s + O*L*o - O*L*l - (O*o - L*l)*S;
e00 = -((O*l-L*l)*S*o - (O*L*o - O*L*l - (L*o-O*l)*S)*s)/D;
e11 = ((O-L)*s - S*(o-l) + (L*o - O*l))/D;
de = -((S*(o-l)-O*o + L*l)*s + (O*l-L*l)*o)/D;
% And then the final equation calculating Gamma per 3-term correction:
G3term = (g-e00)/((g*e11)-de)
*** The Results ***
Gginpez = 0.3288 + 0.7535i
G3term = 0.3288 + 0.7535i
Note: This is not a mathematical proof, but for this example the two methods of error correction give identical results.
Which raises the question: For a one-port VNA, is there an advantage to using the GIN&PEZ equation over the standard 3-term error correction equations?
- Jeff, k6jca
