HP 437B - TYPICAL CALCULATIONS; ACCURACY; MATH ASSUMPTIONS; DERIVATION OF FORMULA FOR V1 - VO

HP 437B
Typical
Calculations
5-12
ADJUSTMENTS
ACCURACY:
DVM Measurements: (Vcomp) +0.018%
(V; — Vo) +0.023%
(R) +0.03%
Math Assumptions: +0.01%
EFFECTIVE EFFICIENCY CAL (NBS): +0.5%
MISMATCH UNCERTAINTY: +0.1%
(Source and Mount SWR <1.05) <+0.7%
MATH ASSUMPTIONS:
ae 2Vcomp (V1 — Vo) + Vo? — Vi?
RF “ (4R) (EFFECTIVE EFFICIENCY)
Assume: Vp*— V,2 = (V; — Vo)?
= (V; =Vg) 7 oe -V,2 + 2V, = Vo?
Want: Vo2 — V,?
«error = (V,2 + 2V, Vo — Vo2) — (Vo? — V2)
if 2V9 (Vi — Vo) < 2Veomp (Vi — Vo) i-e., Vo < Veomp:,
error is negligible.
Vcomp ~ 4 volts. If Vo < 400 xV, error is < 0.01%.
(Typically Vp can be set to <50 nV).
Derivation of Formula for V,; — Vo
eee: 2Vcomp (V, — Vo) + Vo? — Vi?
RF “ (4R) (EFFECTIVE EFFICIENCY)
Desired Ppp = 1 mW = 1073
2Vcomp (V; — Vo) + Vo? — Vi?
= 10-3 SS
(4R) (EFFECTIVE EFFICIENCY)
Let (4R) (EFFECTIVE EFFICIENCY) (1078) = K
Substitute — (V, — Vo)? for Vo? — V,? (see Math Assumptions under Accuracy).
Then 0 = (V,— Vo)? — 2Vcomp (V; — Vo) + K
or V;) — Vo = Vcomp — V_ (Vcomp)? — K