a period is 23ms. with in this period, the modulation signal voltage is

V_{ms}(b,s) = b + ( t - 12.5) s [V]

Max(V_{ms}) = 29.2 [V]   Min(V_{ms} = 0 [V]

on the Gunn Oscillator, there is a mechanical switch, which can adjust the base frequency but changing the length.

f_{base} (l) = 0.61 + 6.433 [GHz]

this data is provided by 3 data point in the manual. the output frequency of the microwave is

f_{out} = f_{base} + F_m ( V_{ms} )

where F_m is the modulation function, that we have to find out. linear?quadratic? at least get a good approximation for it.

the resonance frequency and its FWHM should depend only on the microwave cavity. an a absorption signal can be formulated by a Lorentzian distribution. and this signal will be converted to voltage by a linear conversion factor. ( the green words is an assumption )

L( f_{res} , f_{out} , FWHM_{res} ) = 1/ ( 1 + (\frac { f_{res} - f_{out} } {FWHM_{res}} )^2 )

From the relation between the length and voltage at peak. we can find out the modulation function. since the output frequency is equal to the peak frequency. thus, the output frequency is fixed

f_{out} = f_{res} = 0.6 l + 6.433 + F_m (V_{ms})

if we measure l and V_{ms} we can find out F.

by further measurement,  the modulation is non-linear. That’s also explained the FWHM on the CRO change with frequency. since the FWHM of the microwave cavity should be same and the change of the FWHM in CRO reflected that the gradient of the frequency output. for a linear frequency output, the FWHM should be the same. but if the gradient change with due to the modulation signal, the FWHM will change.

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