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CIRCUIT ANALYSIS OF MIRROR INVERTER-

FED INDUCTION HEATER / COOKER

This chapter is based on the published articles,

1. Dola Sinha, Pradip Kumar Sadhu, Nitai Pal, Mathematical Analysis of the

Mirror Inverter based High Frequency Domestic Induction Cooker,

International Journal of Engineering, Science and Metallurgy, vol. 1, no. 2,

pp. 271-277, 2011.

2. Pradip Kumar Sadhu, Dola Sinha, Nitai Pal and Atanu Bandyopadhyay, A

New Generation IGBT Based High-Frequency Mirror Inverter for Induction

Heating, International Journal of Electrical Engineering and Electrical

Systems, Vol. 03, Issue No. 01, Fall Edition 2010, July 2010 – September

2010, pp. 38-44.

Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 43

In this chapter, a mirror inverter-fed induction cooker (Sadhu et al., 2008, patent

no.216361 and 2010, patent no. 244527, Govt. of India) has been analyzed. Firstly,

an analytical solution has been made. Thereafter, a P-SPICE-based simulation has

been carried out and its results are compared with a real-time experimental model.

Finally, the summary of the chapter is presented.

4.1 Introduction

Mirror inverters are basically half bridge series resonant inverter and commonly

used for medium power induction heating applications. The series-resonant radio-

frequency mirror inverter system has been introduced as a new conception for

induction-heated pipeline or vessel fluid heating in medicinal plant, sterilization

plant and drier for surgical instruments (Sadhu et al., 2001b). Fig. 4.1 illustrates

the mirror inverter circuit. The AC main (220V, 50Hz) is routed through AC filter

before being fed to the bridge rectifier.

Rsn1

Rsn2

Cooking vessel

Vessel support

Harmonic filter

Signal for detection of cooking vessel

220 V, 50 Hz1-Ph

Choke

Brid

ge

rect

ifier

IGBT1

IGBT2C

C1

C2

A

Q R

MN

POB

CXRX

Fig. 4.1: Mirror inverter circuit.

The output of the rectifier is passed through an inductor and a capacitor C as

shown in Fig. 4.2. The capacitor C is of small capacity (5uF) so that the DC

voltage (Vdc) across C does not get leveled. This in-turn help to improve the

overall power factor of the system. The return path of the high frequency current is

through this capacitor C, as at high frequency ‘C’ offers negligible capacitive

reactance ( 1 2cX fC ), where f is in kHz range. Hence, the capacitor C acts as a


short circuited path and allows high frequency current to flow. It also acts as higher

order harmonic filter at the same cost.

Rsn2


Link inductor Cooking pan

From RFI Bridge Rectifier

C

C1

C2

A Q R

MN

Rsn1I G B T 1

IGBT2

POB

Heating coil

Fig. 4.2: Power circuit of radio frequency mirror inverter.

The main power circuit consists of switching devices IGBT1 and IGBT2 and

parallel high resistances Rsn1 and Rsn2 connected one across each device as

shown in Figs. 4.2 and 4.3. The resonant circuit is composed of resonant inductor

(Leq) and capacitors C1 and C2. Resistance Req represents the series equivalent

resistance of the heating coil and the referred value of the load resistance, while Leq

represents the inductance of the same as shown in Fig. 4.4.

Cooking pan

C

A Q R

M

Rsn1

Rsn2

IGBT1

IGBT2

POB

NVdc

Heating coil

Fig. 4.3: Main power circuit of radio frequency mirror inverter.


Rsn2

Vdc

Rsn1

POB

C

C1

C2

A Q R

M

IGBT 1

IGBT 2N

Req Leq

Fig. 4.4: The equivalent circuit of mirror inverter.

Resonance occurs while the inductor Leq and the either of capacitor C1 or

C2 exchange energy between them. As some energy is lost in Req in the form of

induction heating during the process of resonance, the total amount of stored

energy gets reduced in each resonant exchange. However, the energy is again

restored by the switching devices IGBT1 and IGBT2 at the starting of each

resonant cycle.

4.2. Circuit Configuration and Analysis of Mirror Inverter

The single point MN of the radio-frequency mirror inverter circuit as depicted in

Fig. 4.2 is stretched as shown in Fig. 4.5. The non-smooth DC voltage is available

across the points A and B in the above-mentioned circuit.



Rsn2

Rsn1

B

From RFI

Link inductor

Bridge Rectifi

C

C1

C2

A Q R

M

IGBT1

IGBT2

PO

Req Leq

N

Fig. 4.5: Equivalent circuit of the mirror-inverter of with the points NM stretched.

The principle of operation of the circuit is described by dividing it into four

different modes. One resonant cycle is due to combination of Req, Leq, IGBT1 and

C2 and the next resonant cycle is due to Req, Leq, C1 and IGBT2. Both the cycles

get repeated alternatively to push resonant current through the heating coil. These

two cycles are in ON period of IGBTs. Between these two cycles there is an OFF

period of IGBTs. The operating modes of mirror inverter are separately analyzed

below.

4.2.1. Initial mode: When both the IGBTs are OFF and capacitors C1 and

C2 are not initially charged

After full bridge rectification the alternating voltage becomes pulsating DC voltage

of an operating frequency of 100Hz. The series current flowing path is shown in

Fig. 4.6. The switching device IGBT1 and IGBT2 are turned off at t = t0. In this

mode the circuit current flows through the snubber resistors Rsn1 and Rsn2 and

capacitors C1 and C2. As the values of snubber resistors are very high (470kohm),

therefore, maximum current flows through the capacitors. There has been no

conduction through IGBTs.


POB

C

C1

C2

A Q R

M

Rsn1

Rsn2

NVdc

Req Leq

I (t)1

Fig. 4.6: Capacitor charging current path when both switches are OFF.

Here, solid line denotes main working current and dotted line denotes less

magnitude of current flow through the circuit. A small voltage drop appears across

the coil impedance and the rest voltage is equally shared by the capacitor C1 and C2

and this voltage is stored as initial charge voltages (VC1 and VC2 respectively) of

these capacitors C1 and C2. The value of this voltage is almost2dcV .

Depending on the switching conditions of two IGBTs, there exist four

different modes of operation. These are explained below in step-by-step manner.

4.2.2. Mode–1 : When IGBT -1 is ON and IGBT-2 is OFF

The switching device IGBT1 is turned on at t = t1. During this mode, the DC-link

voltage Vdc charges the resonant elements to accumulate energy by supplying

power through IGBT1. At t = t2, the energy transfer from source to inductor (Leq)

and capacitor (C2) gets completed i.e. iL(t1) = Ipeak and VC2(t2) = Vdc. VC2 charged

through the path AQRMNOBA shown in Fig. 4.7. The high frequency alternating

current is flowing through capacitor C because at high frequency the capacitive

reactance offered by C is negligible hence the capacitor acts as a short circuit and

allowing the high frequency current to flow through it. In this mode C1 discharges

from 2dcV

to zero through the path QRMNQ. It is shown that charging current of C2


and discharging current of C1 both follow the same path M to N (as shown in

Fig.4.8).

PB O

IGBT2

C

C1

C2

A Q R

M

IGBT1

NVdc

Req Leq

I (t)1Rsn1

Rsn2

Fig. 4.7: High frequency charging current path of C2.

O PB

IGBT2

C

C1

C2

AQ R

M

IGBT1

NVdc

Req Leq

I (t)2

Rsn1

Rsn2

Fig. 4.8: High frequency discharging current path of C1.


4.2.3. Mode–2: When both the IGBTs are OFF

In this mode, the charge on capacitor C2 will act as a source of energy to drive

current and thus charge C1 from zero to 2dcV and the circuit current will be routed as

indicated in Fig. 4.9. At the end of this mode at t = t3 the capacitor voltage VC2 (t3)

is2dcV . So, C1 and C2 store equal voltage after mode 3.

Vdc

O PB

IGBT2

C

C1

C2

AQ

R

M

IGBT1

N

Req Leq

I(t)Rsn1

Rsn2

Fig. 4.9: High frequency reverse current flowing path from C2.

4.2.4. Mode–3: When IGBT -1 is OFF and IGBT-2 is ON

The switching device IGBT2 is turned on at t = t3. During this mode the DC-link

voltage Vdc lets the resonating elements to accumulate energy by supplying power

through IGBT2. At, t = t4 the energy transfer from source to inductor (Leq) and

capacitor (C1) gets completed i.e. VC1(t4) = Vdc. VC1 charged through the path

AQNMPOBA shown in Fig. 4.10. In this mode C2 discharges from 2dcV to zero

through the path NMPON. It is shown that charging current of C1 and discharging

current of C2 both flow in the same path N to M (refer to Fig. 4.11).


IGBT2

Leq

O

C

C1

C2

AQ R

M

IGBT1

PB

NVdc

Req

I (t)1 Rsn1

Rsn2

Fig. 4.10: High frequency charging current path of C1.

Fig. 4.11: High frequency discharging current path of C2.

4.2.5. Mode–4: When both the IGBTs are OFF

This mode is the second mode (Mode 2) where both the switching devices Q1 and

Q2 are off. The charge on capacitor C1 will now act as a source of energy to drive

IGBT2

Leq

O

C

C1

C2

AQ R

M

IGBT1

PB

NVdc

Req

I (t)2

Rsn1

Rsn2


current and thus charge C2 from zero to 2dcV and the circuit current will be routed as

indicated in Fig. 4.12. At the end of this mode at t = t5 the capacitor voltage VC1

(t5) is2dcV . After end of this mode both C1 and C2 store same voltage i.e.,

2dcV .

IGBT2

C

C1

C2

A Q R

M

IGBT1

POB

NVdc

Req Leq

I (t)1

Rsn2

Rsn1

Fig. 4.12: High frequency reverse current flowing path from C1.

Mode 1 to Mode 4 these four modes will repeat for continuous conduction.

Analyzing all the modes, series current flowing through the heating coil is

expressed as:

11

1 22 1eq

1 1 2 2 2

V dc (t)= cos tanR

cos sin

c eq

eqc eq

C LI t

RC L

Exp k t A k t A k t

(4.1)

1 21 2 1where, and k ( )

2 eq ceq

Rk L C kL

Where Cc = C1 or C2, used according to the operation of C1 or C2.

Moreover, A1 and A2 can be calculated from the initial conditions.


Voltage across heating coil can be obtained using the expression

11

( )( )coil eq eqdI tV R I t L

dt

( 4.2)

The first part of the equation (4.1) shows the steady state condition and the second

part is due to transient condition. The voltage stored in capacitors C1 and C2 during

charging will be expressed as:

1 2 10

1 ( )t

C Cc

V V I t dtC

(4.3)

4.3. Sample Results and Discussions

In this study, currents and voltages have been compared across the heating coil.

Three different methods have been adopted during this study. In the first method,

those two parameters are obtained using the expressions (4.1) and (4.2). In the next

method, a P-SPICE-based simulation has been carried out. On the other hand,

experiments have been conducted with a real induction cooker in the next method.

During this study, the values of snubber resistors (Rsn1 and Rsn2) are considered

as 470kohm each. Coil inductance (Leq) and internal resistance (Req) are taken as

119µH and 0.69ohm, respectively. Capacitors C1 and C2 are each of 0.4µF and C is

5µF. Values of A1 and A2 are calculated from initial values of voltage stored in the

capacitors and obtained as 1.99 and 48.67, respectively. The main supply voltage

Vdc is 220V and applied operating frequency at the main is 50Hz. During the

analytical derivation, an IGBT is replaced by its equivalent circuit as shown in

Fig.4.13.

Fig. 4.13: Equivalent circuit of IGBT.


4.3.1. METHOD 1: Analytical Solution

The four modes (Mode 1 to Mode 4) will repeat according to specified IGBT ON

time and OFF time. The depth of heat penetration on cooking pan is inversely

proportional to operating frequency and the operating frequency is inversed of

operating time period. So, by changing the IGBT ON-OFF time operating

frequency can be changed and thus the heat penetration on cooking pan can be

controlled. The circuit of mirror inverter is analytically analyzed by MS Excel

2007 and different graphs are shown in Figs. 4.14 to 4.17 at different frequency.

Figs. 4.14 and 4.15 show voltage and current across the heating coil at low

frequency.

Fig.4.14. Applied and capacitor voltages with the time at low frequency, when

both switches are OFF.

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.001 0.021 0.041 0.061 0.081 0.101 0.121 0.141 0.161 0.181

Time (sec)

Cur

rent

(Am

p)

Fig.4.15: Series current at low frequency, when both the switches are OFF.


Since the current is very low at low frequency, therefore heat penetration is low.

The complete waveform of current and voltage across the heating coil including

ON and OFF time of each switch at high frequency (38.512 kHz) is shown in Fig.

4.16 and Fig. 4.17.

-20

-15

-10

-5

0

5

10

15

20

0 0.005 0.01 0.015 0.02 0.025 0.03Time (sec)

Coi

l Cur

rent

(A)

Fig. 4.16. Current through heating coil.

-600

-400

-200

0

200

400

600

0 0.005 0.01 0.015 0.02 0.025 0.03

Time (sec.)

Vol

tage

acr

oss c

oil (

V)

Fig. 4.17: Voltage through heating coil.


4.3.2. METHOD 2: PSPICE Simulation

The developed PSPICE schematic circuit diagram is shown in Fig. 4.18. The

circuit simulation has been done with alternating supply voltage of 220 V. A

bridge rectifier is modeled using four diodes of 1N6392 type. Total time period is

taken as 26µsec where IGBT on time is 12μsec and off time is 14µsec. For high

frequency inverter, two IGBTs of HGTP6N50E1D are used. The input parameters

of mirror inverter used for PSPICE simulation are shown in Table 4.1. The

waveform of current through heating coil and waveform of voltage across heating

coil are shown in Figs. 4.19 and 4.20 respectively from PSPICE simulation.

Table 4.1: Input parameters of mirror inverter.

Operating high frequency = 38512Hz Supply Voltage = 220V

Coil inductance, (Leq=L9) = 119µH Coil resistance, (Req=R9)= 0.69 ohm

Capacitors, C10 and C11 = 0.4µF, each Capacitor, C9 = 5µF

Snubber resistors, R10 and R11 =

470kohm, each

IGBT ON and OFF timing = 12 µs

and 14 µs.

L8

100uH

C95uF

L9

119uH

R9

0.69

D201N6392

12

D21

12

D221N63921

2

D231N63921

2

V14

FREQ = 50HzVAMPL = 220V

VOFF = 0

C100.4uF

C110.4uF

0

Z5

HGTP6N50E1D

R10470k

R11470k

0

V15

TD = 0.01us

TF = 2usPW = 12usPER = 26us

V1 = -5V

TR = 2us

V2 = 5V

0

V16

TD = 20.01us

TF = 2usPW = 12usPER = 26us

V1 = -5V

TR = 2us

V2 = 5V

Z6

HGTP6N50E1D

Fig. 4.18: The circuit diagram for PSPICE simulation.


Fig.4.19: The waveform of current through heating coil.

Fig. 4.20: The waveform of voltage across heating coil.


4.3.3. METHOD 3: Real-time Experiment

One prototype model is developed and the real time experimental results from

oscilloscope are plotted. The series current flowing through heating coil and the

voltage appeared across heating coil at continuous conduction of mirror inverter at

high frequency is shown at Fig. 4.21 and Fig.4.22.

Fig. 4.21: The waveform of series current flowing through heating coil.

Fig.4.22: The waveform of voltage across heating coil.


4.4. Summary

In this chapter, H. F. mirror inverter-fed induction cooker has been analyzed in

three ways. Firstly, analytical expressions have been developed for different modes

of operation. In the next case, it is simulated through P-SPICE software and finally

experiments have been carried with a real model. Results obtained through all three

methods are found to be similar. The series current flowing through heating coil

and the voltage across load depends on the resistance and inductance of the heating

coil. So calculation of these parameters is necessary to design an energy efficient

induction cooker.

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