Distortions can be greatly reduced in narrow-band applications by using the second harmonic. The ac behavior of simplified diode amplifier has negative resistance depending on slope of equivalent I-V curve

Buck, D. C.

Cohn, M.

Cooper, H. W.

English

NASA Technical Reports Server

ad 
Lossy 
Dielectric Absorber 
Second Harmonic Tuner, 
Diameter d, 
Fundamental Tuner, 
Diameter d2 
October 1975	 B75-10213 
NASA TECH BRIEF 
Goddard Space Flight Center 	
_4r 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code Kr, Washington, D.C. 20546. 
Microwave Diode Amplifiers With Low Intermodulatlon Distortion 
The problem: 
Microwave tube-type amplifiers with low-to-
intermediate powers in high microwave bands may 
soon be replaced by solid-state diode devices. For 
example, in the band above 5 GHz, Gunn diodes may 
be used if low noise is of prime importance, and 
IMPATT (impact-avalanche-and-transit-time) diodes 
or Read diodes may be used if power output and 
efficiency are more important. The difficulty, 
however, with these nonlinear elements is that with 
improved efficiency there is also an increased 
intermodulation distortion. 
The solution: 
Recent analysis indicates that intermodulation 
distortion can be greatly reduced, at least in 
narrow-band applications, using the second har-
monic.
How it's done: 
A simplified diode amplifier model is used. The 
assumption is that the ac behavior of the diode is like 
that of a tunnel diode: i.e., it has a negative resistance 
depending on the slope of an equivalent I-V curve. 
The diode current I can be expressed as 
'diode = aiVidiode	 (1) 
where ai is an admittance coefficient having dimen-
sions of admittance/volts!-!. 
To obtain expressions for the third-order and 
fifth-order intermodulation (IM) products, it is 
assumed that the two input signals have the form 
V 1 sin c0 1t + V 2 sin co 2t where co w2. Based on this, 
the right side of equation (1) can be expanded to 
Coaxial Diode Cavity, 
Internal Diameter d, 
Coaxial Diode Cavity Amplifier
(continued overleaf) 
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obtain expressions for the third-order IM products 
(i.e., frequencies of the form 2(02 -w and 2w - w2, 
etc.): 
[3/4(a3V 1 2V2) + a5[15/8(V32V23) 
+ 5/4(V 14V2)]]cos (2w ± w2)t 
and a similar term for cos (2w 2
 ± w1)t. 
From the V2 terms, it is obvious that the second 
harmonic signals play an important role in the 
formation of the third-order IM products. The third 
harmonic power is usually very far down from the 
fundamental, assuming one operates a decibel or so 
below saturation. This is a useful assumption for 
avalanche diode amplifiers, as their maximum 
efficiency occurs for input powers below the 
saturation input power. The objective then is to 
reduce or cancel out the second harmonic while not 
appreciably reducing the fundamental at high input 
drive, which should reduce the third-order IM 
products. 
The approach is modeled by using as input voltages 
the two fundamental inputs as before but, in addition, 
their respective second harmonics, including for each 
of their amplitudes V 3 and V4
 and their phases 4) 1 and 
4)2 as independent variables: 
V 1
 cos wit + V 2
 cos w2t + V3
 cos (2w 1t + 01) 
+ V4
 cos (2w 2t + CDz) 
This is done using the diode power series truncated to 
three terms (ai = 0, i >3), with the following result for 
the IM products: 
3/4(a 3V2V 1 2) cos ((02 - 
+ a2(V 2V 3) cos [(W2 - 2w 3)t - 0 1 1 	 (2) 
and a similar expression for Wj - 2w2 . At the same 
time, the fundamental term comes out to be 
[a 1V 1
 + 3/4 (a 3V 1 3)] cos colt 
+ a2V 1V 3
 cos (w it + 4 1)	 (3) 
and a similar expression for the CO2 term. 
The first terms of these expressions (2) and (3) are 
those obtained with no harmonic injection. If it is 
assumed further that the two fundamental signals are 
of equal magnitude (V 1
 = V0, then the second terms 
of expression (2) can be recognized as the cubic term 
correction for the fundamental term for one input, 
which should be of the same order as the first term of 
expression (2). Thus, if we set CD = it, then expression 
(2) can be made very small, while (3) will not change 
B75-10213
appreciably because a 2V 1V 3
 is much smaller than the 
fundamental form a 1V 1. In the ideal case in which 
expression (2) becomes zero, expression (3) with CD = it 
becomes a 1V 1
 cos w it; the two correction terms just 
cancel. Thus, it appears that if a it phase shift can be 
provided for the second harmonic signal generated by 
the diode, the third-order IM products can be greatly 
reduced without appreciably affecting the funda-
mental. 
The proposed coaxial cavity is shown in the 
illustration with the diode at one end where the 
impedance is low. Toward the other end of the cavity, 
two tuning cylinders are used; their diameters 
determine the amount of reflection of the funda-
mental and second harmonic signals. The axial 
lengths of the cylinders determine the fundamental 
and second harmonic frequencies, and their positions 
affect the phase of the reflections. 
The length of the fundamental tuner is one-fourth 
the wavelength of the fundamental frequency and 
one-half the wavelength of the second harmonic 
frequency. Thus as the second harmonic is transmit-
ted from the diode, it passes the fundamental tuner 
and is reflected off the second harmonic tuner (which 
has a length of one-fourth the wavelength of the 
second harmonic). The fundamental frequency 
reflects off the fundamental tuner, thus defining the 
phase of the fundamental frequency. The phase of the 
second harmonic, generated by the square (a 2) term of 
the diode, is determined by the harmonic tuner. Its 
magnitude is, again, determined by the diameter d3 
and the internal diameter of the coaxial diode cavity 
d 1 . The result is that the lundamental and the second 
harmonic are tuned independently of each other. 
Note: 
No further documentation is available. Specific 
questions, however, may be directed to: 
Technology Utilization Officer 
Goddard Space Flight Center 
Code 704.1 
Greenbelt, Maryland 20771 
Reference: B75-10213 
Patent status: 
NASA has decided not to apply for a patent. 
Source: Herbert W. Cooper, 
Marvin Cohn, and Daniel C. Buck of

Westinghouse Electric Corp. 
(GSC-11668) 
Category: 01 (Electronics - Components

and Circuitry)


Microwave diode amplifiers with low intermodulation distortion

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