Tapered Impedence Transformers for Pulse Type Noise Generators

72 Pages·2.712 MB·English

by  Hammerle, Kenneth John

PURDUE UNIVERSITY
THIS IS TO CERTEPY THAT THE THESIS PREPARED UNDER MY SUPERVISION
Kenneth John Hamnerle
e n title d Tapered Impedance Transformers for Pulse Type Noise
Generators
COMPLIES WITH THE UNIVERSITY REGULATIONS ON GRADUATION THESES
AND IS APPROVED BY ME AS FULFILLING THIS PART OF THE REQUIREMENTS
FOR THE DEGREE OF
Doctor of Philosophy
PROFESSOR IN CHARGE OF TRESIS
HEÆD of School or Department
19
TO THE LIBRARIAN:-----
ML
THIS THESIS IS NOT TO BE REGARDED AS CONFIDENTIAL.

TAPERED IMPEDANCE TRANSFORMERS FOR
PULSE TYPE NOISE GENERATORS
A Thesis
Submitted, to the Faculty
©f
Purdue University
by
Kenneth John Hammerle
In Partial Fulfillment of the
Requirements for the Degree
©f
Doctor of Philosophy
June, 195>1
ProQuest Number: 27714218
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ABSTRACT
The purpose of this thesis is to analyze certain devices which may
be used in conjunction with a pulse-type noise generator in order to in­
crease its useful output* The analysis consists of finding the fre­
quency spectrum of the impulse produced when a step voltage is applied
to a suitably terminated transmission line*
Throughout the entire analysis, one end of the transmission line
(called the discharge line) is assumed to be open-circuited* The other
end ©f the line is assumed to be terminated variously. The first termi­
nation considered is one consisting of a resistance in series with a
capacitance* The second termination considered consists of a capaci­
tance in series with a tapered impedance transformer which is itself
terminated with a resistance. The last termination considered is sim­
ilar to the second, but an additional capacitor is placed in series
with the resistance at the receiving end of the tapered transformer*
The theoretical frequency spectra are obtained for dissipation-
less lines when terminated as described* The effects of dissipation
are then discussed in seme detail*
Finally some specifications are given for the construction of a
typical noise generator and appropriate calculations are made*
AGKNOWLHGMMTS
The anther gratefully acknowledges the encouragement, and guidance
®f PrefesSbr G* B. Cooper, under whose supervision this project was
carried ferWârd* He also acknowledges the assistance of Miss V. A*
Qhlson whesè untiring efforts were invaluable in the carrying out of
certain tedious computations* Finally, he acknowledges the assistance
of Mr* R. K* Cheng who liberally contributed his time and skill to the
task of lettering the large number of equations appearing in this thesis*
TABLE OF CONTENTS
Phge
ABSTRACT ................. ................................
INTBODUCTXUN....... 1
oomimmTiom ..... k
UNIEOBK TRANSMISSION LINE WITH R-C TERMINATION.......... 3
TAPERED IMPEDANCE TRANSFORMERS ......................... 10
A PreUiaiiiary Diseussion............... 18
Liae with Linear Taper .... 19
Traaeaissien Line with Ejqpenential Taper ..................... 23
Neise Generater with Tapered Transformer ........ 29
Seme Mathematical Difficulties Shcountered in Computing Voltage
Spectra........ 3Î4
SOME CALCULATED SPECTRA......... 37
DISSIPATION.......... hB
A TYPICAL NOISE GENERATOR .... 57
BIBLIOGRAPHY....... 63
' MStf OF FT OU RES
Figure Page
lc Terminated Transodsaien Line and its Equivalent ....... 2
2. Voltage Applied t® Circuit ©f Figure 1 ............... 5
3* Frequency Spectra far Rr-C Terminated Lime ...... 10
k* Frequency Spectra for R-C Terminated line 11
Frequency Spectra for R-C Terminated line. .................. 12
6. frequency Spectrum fer Resistance Terminated Line ...... .... 13
V* Incremental Length of Dissipationless Transmission line ..... 21
8. Input Impedance Characteristic for Resistance Terminated
Exponential Transformer .............. ................... 28
9<> Input Impedance Characteristic for R-C Terminated Exponential
Tranfifomer ... ....... . ...... .. ........ 30
10. Frequent Speetra fer line with Exponential Transformer .. .. 38
11* Frequency Spectra fer Line with Exponential Transformer ..... 39
12* Frequency Spectrum for Lin© with Exponential Transformer .... ItO
13. Frequency Speetruza for line with Exponential Transformer .... Ul
Ik* lower Frequenoy Lirait of Flat Portion of Speetrmn ........... U2
15. Frequency Speetra for Line with Exponential Transformer ..... kh
16* Froqueney Spectrum for line with Exponential Transformer .... h5
17. Frequency Spectrum for Line with Exponential Transformer .... L6
1
TAPERED IMPEDANCE TRANSFORMERS FOR
PULSE TYPE NOISE GENERATORS
INTRODUCTION
Investigators associated with the Engineering Experiment Station
at Purdue University have succeeded in developing pulse type noise
generators which are capable of producing pulses ©f such shape and
duration that their spectra contain useful energy components ©f all
frequencies in a band extending from zero to the lower ranges of the
uhf region* The design of these generators proceeded from the math­
ematical analysis of certain pulse forming circuits « The mathematical
analysis was based upon a physical interpretation of the Fourier in­
tegral and the Laplace transform* A suitable interpretation of the
Laplace transforms representing the voltage pulses at the output term­
inals of various proposed generators led to the selection of the cir­
cuit and its physical constants which produced a frequency spectrum
most nearly approaching the ideal constant amplitude spectrum*
Although the present thesis deals with noise generators which are
generically related to these described in Reference 1# the mathematical
approach is somewhat different* The frequency spectrum of a voltage
pulse applied in series with a transmission line and its termination.
Figure la, is computed from the Fourier integral 2 representing this
^ Cooper, G, R», Analysis of Waveforms for a Standard Radio Noise Gen­
erator, Fh» D* thesis, June, 19U9* Purdue University*
2 Gardner, M. F* and Barnes, J* L», Transients in Linear Systems, John
Wiley and Sens, New York, 19U2, pp* 99-iolu "
2
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