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# Optimization Method for High Efficiency Microwave Frequency Doublers

IP.com Disclosure Number: IPCOM000096057D
Original Publication Date: 1964-Nov-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 3 page(s) / 25K

IBM

Rutz, EM: AUTHOR

## Abstract

Microwave frequency doublers with varactor diode 10 in microwave transmission line 12 having input and output filters 14 and 16 are designed by an analytical technique. By this, the operating region of highest efficiency for diode 10 is chosen by evaluating input power, line characteristic impedance, input and output impedances, and distance 18 between filter 16 and diode 10.

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Optimization Method for High Efficiency Microwave Frequency Doublers

Microwave frequency doublers with varactor diode 10 in microwave transmission line 12 having input and output filters 14 and 16 are designed by an analytical technique. By this, the operating region of highest efficiency for diode 10 is chosen by evaluating input power, line characteristic impedance, input and output impedances, and distance 18 between filter 16 and diode 10.

Input power to the frequency doubler, at the fundamental frequency, is the sum of the real power in the diode 10 junction and the power loss in the diode's spreading resistance R at the fundamental frequency. Real power in the diode 10 junction is the power that becomes converted from the fundamental frequency to the second harmonic. It is the same for the fundamental and for the harmonic and is given by P= 1/(2 pi/2/) >1/(1-lambda)|wc(mi) (v(B) + phi)/2/1(1) where C(min) in is the diode capacitance at the breakdown voltage, V(B) the breakdown voltage, phi the contact potential, lambda the exponent that characterizes the diode's non-linearity, and rho(1) the normalized real power.

The power loss in R at the fundamental frequency is given by L(w)=(1/2)I/2/(w)R(s) where I(w)= J >1/(1-lambda) wc(min)(V(B)+ phi)(b cos w t-c sin wt) where b and c are Fourier coefficients of the Fourier series representing the charge on the diode junction.

To feed input power P into diode 10, the characteristic impedance of line 12 must be matched at the fundamental frequency to the resistive component of diode impedance at this particular power level. The resistive component is the ratio of the real power in diode 10 to the square of the displacement current. The characteristic impedance of line 12 at the fundamental frequency, for matched condition, then becomes (Z(0))(w) =2(P+L(w))/I/2/(w).

Waves at the fundamental frequency, as well as at the second harmonic, are present at the diode 10 location. Line 12 must be matched to the resistive component of the diode impedance at the second harmonic as well. All the power in the second harmonic can then be taken from the diode junction and directed to the load. The characteristic impedance of line 12 at the second harmonic, for matched conditions, must be made equal to (Z(0))(2w)=2(P-L(2W))/I/2/(2w) where I(2w) =J >1/(1-lambda)|wc(min)(V(B)+ phi)(2d cos 2wt-2B sin 2wt)and where d and e are Fourier coefficients of the Fourier series representing the charge on the diode 10 junction and L(2w)=(1/2)I/2/(2w/R(s)).

The tr...