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A novel structure of transmission line pulse transformer with mutually coupled
windings
Binxiong Yu, Jiancang Su, Rui Li, Liang Zhao, Xibo Zhang, and Junjie Wang
Citation: Review of Scientific Instruments 85, 035110 (2014); doi: 10.1063/1.4867250
View online: http://dx.doi.org/10.1063/1.4867250
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/3?ver=pdfcov
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 035110 (2014)
A novel structure of transmission line pulse transformer with mutually
coupled windings
Binxiong Yu,a) Jiancang Su, Rui Li, Liang Zhao, Xibo Zhang, and Junjie Wang
Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology,
Xi’an 710024, People’s Republic of China
(Received 29 September 2013; accepted 18 February 2014; published online 18 March 2014)
A novel structure of transmission line transformer (TLT) with mutually coupled windings is described
in this paper. All transmission lines except the first stage of the transformer are wound on a com-
mon ferrite core for the TLT with this structure. A referral method was introduced to analyze the
TLT with this structure, and an analytic expression of the step response was derived. It is shown
that a TLT with this structure has a significantly slower droop rate than a TLT with other winding
structures and the number of ferrite cores needed is largely reduced. A four-stage TLT with this
structure was developed, whose input and output impedance were 4.2 and 67.7 , respectively.
A frequency response test of the TLT was carried out. The test results showed that pulse response
time of the TLT is several nanoseconds. The TLT described in this paper has the potential to be
used as a rectangle pulse transformer with very fast response time. © 2014 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4867250]
I. INTRODUCTION
Transmission line transformers (TLTs) with good fre-
quency characteristics and compact structures are widely used
in high power pulse technology field.1–8Some high power
pulse generators based on TLTs can output voltage pulses
with amplitudes of 100 kV, repetition-rates of 1000 pulses
per second (pps). Linear TLTs do not use ferrite cores and
all their transmission lines are kept straight. They have very
wide bandwidth, and can be used to construct short pulse gen-
erator in radio frequency (r.f.) and flash X ray applications.1,2
As pulse widths of delivered pulses get wider, the influence of
parasitic inductance becomes more and more serious, which
can cause gain loss of the TLT.9To avoid this problem, all
transmission lines of the TLT except the first stage were
wound inductively with ferrite cores. TLTs with ferrite cores
are called wound TLTs. According to the coupling intensity
between the windings, wound TLTs can be divided into two
types, the TLT without coupled windings and TLT with mutu-
ally coupled windings. Graneau and Smith analyzed the two
TLT winding models using a referral method,8and the results
showed that a slower droop rate could be achieved by using
TLT with mutually coupled windings. Reference 8introduced
a 3-stage TLT model with mutually coupled windings. In this
device the top stage had two windings, one of which was mu-
tually coupled to the winding of the second stage. With this
method, more than one ferrite core is required, and n-1 pieces
of ferrites are needed for a TLT with n stages. In this paper,
a novel model of transmission line transformer with mutually
coupled windings is introduced. All transmission lines except
the first stage are wound on a common ferrite core. With this
structure, the TLT has a slower droop rates, and only one fer-
rite core is used.
a)E-mail: rucieryi12@gmail.com
II. PRINCIPLE
Fig. 1shows the structure of the TLT with a common
ferrite core. The 2nd and 3rd stage transmission lines of the
TLT are wound on a common ferrite core. Vstands for the
input voltage of the TLT, and Z0represents the characteristic
impedance of each transmission line. I1and I2stand for the
unbalanced current of the first and the second stage secondary
parasitic lines, respectively. Mij are the mutual inductance be-
tween the ith stage winding and the jth stage winding. As the
unbalanced currents in parasitic lines magnetize the ferrite,
the induced voltages are generated across the windings wound
on the ferrite core according to Faraday’s law. Assuming the
turn number of the ith stage winding is Ni, and induced volt-
age on the ith stage winding is Vi(i =2, 3), then,
V2:V3=N2:N3.(1)
According to Fig. 1, it is found that there is a potential
drop of 2Vacross the 3rd stage winding. Similarly, there is a
potential drop of Vacross the 2nd stage winding, so
N2:N3=1:2.(2)
For an n-stage TLT with a common ferrite, Turns of the wind-
ings on the ferrite core satisfy
N2:N3:......N
n=1:2:......n−1.(3)
Now, the referral method is used to analyze a 3-stage TLT
with this structure. The first stage is not wound on the ferrite,
and has no mutual inductances with other stages. So it can
be obtained that Mi1 =M1i =0(i=1, 2, 3). According to
Faraday’s law, it can be derived that
3
j=2Mij −Mij −1dIj−1/dt =(i−1)Vi=2,3.(4)
Assuming that the self-inductance of the first winding M22
is L0, and coupling coefficients between windings are k
0034-6748/2014/85(3)/035110/4/$30.00 © 2014 AIP Publishing LLC85, 035110-1
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035110-2 Yu
et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 1. A three-stage transmission line transformer with single magnetic
core.
(leakage inductance of all the windings is considered to be
equal), namely,
Mij =(i−1) (j−1)kL0i= j
Mij =(i−1)2L0i=j
.(5)
So, Eq. (4) can be simplified as
(2 −k)dI2/dt +kdI1/dt =V/L
0
(2k−1)dI2/dt +dI1/dt =V/L
0
.(6)
The solution to Eq. (6) can be got by Cramer’s law, and is
shown below
di2/dt =V/2(k+1)L0
di1/dt =3V/2(k+1)L0
.(7)
When kgoes to 1, it is found that
di2/dt =V/4L0
di1/dt =3V/4L0
.(8)
Now, it can be derived the equivalent schematics of Fig. 1
which is shown in Figs. 2(a) and 2(b).Fig.2(a) shows equiva-
lent circuit of the transformer output, and Fig. 2(b) shows the
equivalent circuit of the transformer referred to the primary.
According to Ref. 8, the output voltage of this transformer on
a matched load was found to be as follows when a voltage
step source of amplitude Vis fed
Vo=3Vexp −5Z0t
24L0.(9)
This winding technique can be extended in an n-stage de-
vice by winding all but the bottom line on one core, and turns
of the windings on the core satisfy Eq. (3). The general ex-
pression for an n-stage transformer of this type can be derived
similarly by Cramer’s law, which is presented as Eq. (10),
Vo=nV exp −(n+2)Z0t
8nL0.(10)
However, the output voltage of a TLT with mutually coupled
windings mentioned in Ref. 8whose structure was introduced
in Sec. Iwas found to be
Vo=nV exp −(n−1)Z0t
2nL0.(11)
Comparing Eq. (10) with Eq. (11) together, it is found that
a TLT with structure mentioned in this paper had a slower
FIG. 2. Equivalent schematics of a three-stage TLT. (a) Equivalent circuit of
the transformer output; (b) Equivalent circuit of the transformer referred to
the primary.
droop rate than a TLT with the structure mentioned in Ref. 8
when L0and Z0are kept the same, respectively. Addition-
ally, when L0is the same, a TLT with structure mentioned in
Ref. 8requires n-1 pieces of ferrite cores, each one of which
had the same size as the ferrite core used in a TLT with struc-
ture in this paper. So the number of cores is largely reduced
when the winding structure in this paper is used to build a
TLT with stages larger than 2.
III. PERFORMANCE
In order to test the rectangular pulse response character-
istics of the TLT with a common ferrite core, a four-stage TLT
using cables was developed. Each stage of the TLT consisted
of 3 cables in parallel with a length of 2 m. the outer diameters
of the cables were 5 mm, and the characteristic impedances
FIG. 3. Schematic for measuring pulse response characteristic of TLT.
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035110-3 Yu
et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 4. Measured results of response characteristic of the TLT. (a) Measured waveform when a 100 ns pulse is injected. (b) Measured waveform when a 300 μs
pulse is injected.
were 50 . The impedances of transmission lines of the TLT
were 16.7 , and the input and the output impedances of the
TLT were 4.2 and 67.7 , respectively. Relative perme-
ability of the used ferrite core was 1000, and the response
frequency ranged from 0 to 1 MHz. An arbitrary pulse gener-
ator, agilent 33220 A was used as a rectangular pulse source,
which can generate pulses with a rise and a fall time of 10 ns.
The testing circuit is shown in Fig. 3. In this figure, R1(50 )
represents the internal resistance of the pulse generator. R2,
whose resistance was 16.7 , together with the 50 sam-
pling resistance of the oscilloscope, composed a 66.7 load
which was matched with the TLT. The input and the observed
output pulse waveforms are shown in Fig. 4. From the figure,
amplitude of the input voltage pulse was 0.14 V, and ampli-
tude of the observed pulse was 0.41 V, Considering voltage
dividing function of R2, the observed voltage was only three
quarters of the voltage amplitude on the matched load. So the
output voltage of the TLT on the matched load was 0.55 V.
it was found that output voltage of the TLT was 3.93 times
of the input. So transmission efficiency of the TLT was 98%.
Besides, from the figure, it was found that output waveform
of the TLT had almost the same temporal shape as the input,
and its rise time was 10 ns, which demonstrated that the devel-
oped TLT has a very good frequency response characteristic.
A rectangular pulse with a pulse width of 300 μs was also in-
jected into the transformer to test its ability to maintain “flat
top” over a relatively long time scale. The output waveform
is shown in Fig. 4(b). From this figure, a droop of 90%–10%
can be obtained to response a pulse with width of 65.5 μs. The
theoretic droop of the TLT was derived the same as,8which
was
τ=2.19 nL0(50 +Z0/n)
50 (n+2)Z0
,(12)
where L0was measured by a RLC meter, whose value was
109 μH. So, the calculated value of the droop was 40.1 μs.
It was found the observed droop was even slower than the
theoretic value. The theoretic value was not confirmed to be
the observed results because we assumed that leakage induc-
tances of windings of the TLT were the same during analysis.
Factually, the leakage inductances of windings were different.
So, the result of the theoretic value was not accurate enough.
A small rectangular pulse generator was developed based
on the TLT technology. The structure of the generator is
shown in Fig. 5. The pulse forming network (PFN) whose
impedance was 5 was charged to 5.5 kV by a DC voltage
source in order to inject a voltage pulse of 2.5 kV into the
transformer. R3is the charging resistance, whose value was 1
k. The load resistance, R4, is 66.7 , which is matched to the
output impedance of the TLT. A HV probe, Tektronix 6015A,
was used to measure the voltage waveform of the load, and
the measured waveform is shown in Fig. 6. From the figure, it
was found that the amplitude of the output pulse was close to
10 kV, and its rise time was only 8 ns.
FIG. 5. Structure of pulsed power source based on TLT.
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035110-4 Yu
et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 6. Output voltage waveform of pulse generator.
IV. CONCLUSIONS
A novel structure of transmission line transformer was
presented in this paper. The TLTs with this structure have
several advantages. First, it has a significantly slower droop
rate than the TLTs mentioned in literatures. Second, the num-
ber of ferrite core needed to build the TLT is largely reduced.
Finally, it is easy to realize compactness. A TLT with a low
impedance was developed, whose input and out impedance
were 4.2 and 66.7 , respectively. The pulse response time
of the TLT was only several nanoseconds, and the transmis-
sion efficiency of the TLT was 98%.
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