U - Power Electronics Systems Laboratory

Power Electronic Systems Laboratory Power Electronic Systems 1
Prof. Dr. J.W. Kolar Exercise No. 6
Last Name, First Name
Passed
Resonant Converter II
Diagram 1 shows a circuit for the inductive heating of metals with the specifications shown below. The
circuit has no load, i.e. there is no item in inductor L, and operates with f = 100 kHz and a duty cycle of
50%, i.e. 50% of the time is T + and 50% T - activated.
Disregard the damping resulting from the parasitic ohmic resistances. Furthermore, assume that the
transformer, the power transistors and the diodes are operating ideally in your calculations.
i DC
U DC
T +
C DC
T -
D +
D -
u
C
inductor
u C
i L
L
ideal transformer
10:1
Diagram 1 – Resonant Converter
Specifications:
Input voltage:
U 1 = 540 V
Inductor inductance: L = 0.57 µH
Resonant circuit capacity
C = 100 nF
Transformation ratio of the transformer: n = 10:1
You must answer questions 1-4 at least to pass the exercise.
1) What are the average values of the capacitor voltage u C and the current i L ?
Make a drawing of the waveform of the current i L and the capacitor voltage u C in the diagram below
where u C (t=0) = 0 V and i L (t=0)= 0 A and the transistor T + is switched on at time zero for T/4 =
1/(4f), i.e. a quarter cycle duration. In addition, indicate when which semiconductor is conducting
current.
2) Consider the fundamental component of the oscillation and the DC-part of the voltage u. Determine
the fundamental component of the oscillation and the DC-part of the capacitor voltage u C and the
current i L by use of the complex alternating current calculation and the superposition theorem. Add
the fundamental oscillation trajectory to a u C -Zi L -diagram.

Power Electronic Systems Laboratory Power Electronic Systems 1
Prof. Dr. J.W. Kolar Exercise No. 6
3) Now make a u C -Zi L diagram for no-load (steady-state operation, scale: 90 V/cm) and f = 100 kHz
for the circuit in diagram 1 (above) in the coordinate system below.
How does the diagram change when the operating frequency is doubled to f = 200 kHz?
4) Calculate the dependency of the RMS value of the current i L at no load from the operating
frequency normalised to the resonance frequency of the resonant circuit f/f 0 (consider only the
above resonant operation f/f 0 > 1).
Note: Determine the peak value of i L as a function of the parameter f/f 0 , Z o (characteristic
impedance of the resonant circuit) and U DC . As the current i L , according to question 1), is
approximately triangularly shaped, the RMS value can be easily determined out of the
peak value.
5) Can the transistors (and anti-parallel diodes) used in the circuit be replaced by thyristors?
Justify your answer on the basis of the waveforms determined in question 1).
6) How can the optimal operating frequency f in relation to f 0 be selected regarding a power output to
the load (an item in the inductor coil heated by the eddy currents) in order to keep the load on the
inverter as small as possible?
7) How large is the maximum stored energy in the resonant circuit in the case of above resonance
and how can this be read from the u C -Zi L diagram in question 3).
8) What does the u C -Zi L diagram for below-resonance operation (f = 50 kHz) look like?
(Complete the diagram in the drawing after question 3)).

i / u / i
L C DC
Task 1)
540V
u
T on +
270V
5µs
10µs
t
T/2 = 1/(2f)
i DC
U DC
T +
C DC
T -
D +
D -
u
C
inductor
u C
i L
L
ideal transformer
10:1

Task 3) and 8)
Z*i L
270V 540V 1080V
540V
u C
-540V
-540V
i DC
U DC
T +
C DC
T -
D +
D -
u
C
inductor
u C
i L
L
ideal transformer
10:1