# FFT Analysis of a Series Loaded Resonant Converter-Based Power Supply for Pulsed Power Applications

Authors: R. B. Jadeja; S. A. Kanitkar; Anurag Shyam
Journal: International Journal of Plasma Science and Engineering
 (2008)

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## Abstract

An impulse power supply has been designed, simulated, and tested in order to feed the primary of a high-frequency transformer. Pulse power system has been widely used for plasma applications. The operational principle of the pulse power system is that the energy from the input source is stored in the capacitor bank device through a dc-dc converter. Then, when a discharging signal is given, the stored energy is released to the load. The new family of ZCS converters is suitable for high-power applications using insulated gate bipolar transistors (IGBTs).  The power converter can achieve zero switching with the aid of high-frequency transformer. The device is capable of charging a 0.1μF capacitor up to 5 kV which accounts for a charging power of 5 kJ/s. The novel control algorithm is achieved which eminently considers the nonlinear control characteristics of impulse power supply. The required charging voltage, together with the constraint on the charging time, translates into a required maximum power of 10 kW reduced in this initial version to 5 kW. The difficulty to reliably control such a power at the high-voltage side practically forbids any approach featuring a more or less stabilized DC high-voltage to be generated from a conventional 50 Hz transformer through rectification.


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## Body

## 1. Introduction

For many  years, power electronics in the
high-power area was performed  with slow semiconductor switches like MOSFET and
BJT. The IGBT is a relatively  new power semiconductor device, which provides
the best features of both the MOSFET and the BJT [1]. Its advantages are low power,
voltage-driven turn on and turn off, gate impedance as high as MOSFET, low-conduction losses, and positive temperature coefficient. The device will not
experience thermal run-away as of BJTs. Possibility to use either integrated or
external antiparallel diode. Recent improvements in high-power semiconductor
technology have given switching performance similar to that of the IGBTs to the
high-power area through the advancement of the IGBTs. This paper explains the
internal dynamics [2] of IGBT behavior in zero current switching circuit
topologies. The impulse power supply described in this paper has been initially
built to provide a charging power of 5 KW only. The impulse power supply differs
from conventional power supply in that capacitor charging requires operation
over a wide range of load conditions varying from nearly short circuit, when
the capacitor has no charge, to nearly open circuit, when the capacitor is
almost fully charged. This kind of performance can be best achieved  by supplying a constant
charging current. The instantaneous output power then is minimum at the charge
beginning and maximum at the charge end. The paper proposes a novel topological
circuit of stable voltage source power converter using latest IGBTs (IRG4PH40PUD).


## 2. System Design

The required charging voltage, together with the constraint of the charging time,
translates into a required maximum power of 10 KW reduced in this initial
version to 5 KW as shown in Figure1. The difficulty to reliably control such a
power at the high-voltage side practically forbids any approach featuring a
more or less stabilized DC high-voltage to be generated from a conventional 50 Hz
transformer through rectification, as shown in Figure 2.Figure 1
Power supply architecture.Figure 2
Hardware testing.Instead, it is more attractive to utilize a high-frequency converter performing the
regulation at the low-voltage side of its step-up  transformer and charging the
primary capacitor with high-voltage pulses. Such a device is not capable of
providing  a stabilized DC voltage and, therefore, can be merely regarded as an
impulse power supply. The modular architecture allows simplifying the problem
of the construction of the 20 KV, 5 KW step-up transformers and the selection of
electronic  components suitable to drive it. A subdivision of the power supply
into four identical blocks reduces the requirements to four 5 KV, 1.25 KW
modules, which can be implemented with off-the-shelf components.The design is scalable, as more converter modules can be added in series to reach a
higher charging voltage, with their output floating respect to ground. The capacitor
charging power supply (CCPS) output is internally center-tapped to ground one
of the output leads. Hence it assumes a maximum potential of +10 KV while the other
one assumes a minimum potential of −10 KV (respect to
ground). This strategy increases safety and allows reducing to one half (10 KV DC) the
insulation requirement of assemblies and wiring. A single controller
module samples the charging voltage and drives the converter. It is responsible
for synchronizing the charge with external events and suspending the charging
pulses when a predetermined voltage is reached. Galvanic isolation at several
points is either required or desirable in order to reduce noise and
interference.


## 3. High-Frequency Converter

The basic block diagram of one converter module as shown in Figure3. The converter modules are fed with 560 V DC obtained by rectifying 400 V AC from
the mains. A full-bridge switch drives a step-up transformer with a 9 : 1 turns
ratio in order to reach a rectified output voltage of about 5 KV DC. The switch
commutation is externally driven by the controller (UC3860) module, according
to the capacitor charge state as shown in Figure 4.Figure 3
Basic block diagram of one converter module.Figure 4
Schematic diagram of the high-frequency converter.The topology selected for the converter is the series-loaded resonant (SLR) [3, 4].
In this configuration, the switches and resonant components L and C are
connected to the low-voltage side of the transformer. Only the rectifiers on
the transformer secondary must have high-voltage ratings. By closing, in proper
order, the switches in pairs, pulses of alternate polarity are applied to the
transformer using a high-turn ratio, high-voltage pulses are generated at the
secondary, increasing the capacitor charge.


## 4. Theory of Operation

The characteristic impedanceZ0 of the bridge load is given by(1)Z0=LCeq.And its resonance frequencyf0 is given by (2)f0=12πLCeq,Ceq is the series combination of capacitors C and Cc′, where Cc′ is the equivalent
capacitance Cc reflected in the primary [5–8](3)Cc′=(N2N1)2Cc=81⋅Cc.Usually
in high-voltage applications,Cc (0.1 μF in our case) is at least
order of magnitude greater than C. While its contribution is negligible:(4)Ceq=11/C+1/Cc′≈C.Therefore,Z0 and f0 are uniquely defined by C and L. Operating the
circuit at a frequency fs<f0/2, all switches and antiparallel
diodes turn on and off at zero current. Using a frequency f0/2<fs<f0, the diodes turn off and the switches turn on happen at a current greater than zero. Conversely,
for fs>f0, the diodes turn  on and the switches turn
off at a current greater than zero [9].


## 5. Results

The maximum peak reverse current flowing through the diodes when one switch pair is
open is given by(5)IOFFmax=VinZ0.The above value is assumed at the beginning of charging and drops down to zero at
the end of charge. This is due to the voltage reversal effect across the load
terminals, caused by the voltage present on the capacitor under charge.
Conversely, the maximum peak current flowing in the load C2 and L1 when a
switch pair is closed is given by(6)IONmax=2VinZ0=−2IOFFmax.This value is reached only at the end of the charge and is due to the energy
accumulated in the resonant load C2 and L1 at charge beginning isION=−IOFFmax. Therefore, the  SLR converter switches must be capable to
stand IONmax, while the diodes can be sized to operate at IOFFmax only:(7)IOFFmax=−VinZ0=−VinL1/C2=−5600.07×10−3/0.037×10−6=−13A,IONmax=−2IOFFmax.The RMS capacitor charging current can be calculated directly from the capacitor
charging rate. WhereΔV is the difference between output and input of the transformer:
(8)ICrms=C1ΔVΔt=0.1×10−6×5000600×10−6=832mA.The RMS current in the resonant load and transformer primaryI1rmscan
be calculated by balancing the average power between capacitor (PCave)
and load (PLave):(9)PCave=ICrms⋅ΔV2=832×10−3×50002=2080W,(10)I1rms=PLaveVin=PCaveVin=2080560=3.714A,(11)P=0.5⋅C1⋅(ΔV)2Δt=0.5×0.1×10−6×50002600×10−6=2083W.The theoretical value of voltage is calculated by the following equation:(12)N1=15turns,N2=N1V2V1=155000560≈135turns,N1=15turns,V2=V1N2N1=56013515=5040volts.The theoretical power value as per (11) is more than sufficient to ensure an actual
value greater than the targeted 1.25 KW.For approximate analysis using complex ac-circuit analysis [10–13] in this method,
fundamental components of the waveforms are used for voltages and currents.
This method cannot predict the various voltage and current waveforms
appropriately, and the accuracy reduces as the switching frequency is away from
resonance frequency (as in variable frequency-controlled converters) or as the
duty ratio decreases (as in fixed frequency-controlled converters).For Fourier series method or frequency domain approach [12, 13] method, all the predominant
harmonics are taken into account. This method is simple and gives good results.The output wave form is taken on the TPS2014 digital
storage oscilloscope. The output voltage of transformer is as shown in Figure5.
The signal via digital storage oscilloscope (DSO) is analyzed in FFT toolbox of
MATLAB. The commutation takes place at zero current; unwanted spikes and noise
are present due to parasitic capacitance, PCB traces impendence, reverse
recovery time of the antiparallel diodes, electromagnetic radiation, and
coupling within the converter PCB. The noise signal can be seen from the fft wave form.Output voltage across transformer.
(a)(b)The charging voltage across the capacitor is shown in Figure6. Figure 7 shows the
input voltage to transformer. The output voltage across resonant controller UC3860
which drives the IGBT (IRG4PH40PUD) is shown in Figure 8. We
can clearly see that the DC and first-order harmonic components are high [13].
The higher-order harmonic components are reduced very quickly [13]. The total
harmonic distortion (THD) is small:(13)THD=VacVfund=∑n=2∞Vn2Vfund.Figure 6
Waveform of capacitor charging.Transformer primary voltage with FFT.
(a)(b)Output wave form of controller IC uc 3860.
(a)(b)The maximum peak reverses current flowing through the diode when one pair switch is
open is −13 amps. TheIONmax is 26 amps. From Figure 9, we can see
that the efficiency of ZCS-PWM is much better [14] than that of ordinary PWM
because the losses in the ZCS decrease due to soft switching.Figure 9
Comparison of efficiency of PWM and ZCS-PWM.


## 6. Conclusion

With the new device technology recently developed, the performance of high-power
converters can be improved dramatically in terms of dynamics, efficiency, size,
and protection, due to the improved switching speed and the removal of the
turn-off snubber. The series load resonant topology choice for the switching
converter module resulted in minimized switching loss and reduced size of the
heat sink. The proposed schemes have several advantages over conventional
scheme such as simple operation, easy analysis and control, and improved
effiency.



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*Source: 284549-2008-04-24.xml*