How should one
design a 50kHz, 1200VA
resonance transformer
for a LLC converter
Typical application schemas of a resonamce
transformer
3 typical application schemas of the resonance transformers are shown
in the pictures Fig 1, Fig 2 and Fig 3
In the Fig 1 is shown an AC.AC converter with
the resonance transformer.
The Fig 2 is used as an ACDC converter for very low DCoutput
voltage,
The most used ACDC converter with the resonance transformer is
shown in the Fig 3
The input voltage Uin is normally created by PWM .
The capacitor C and the main inductance Lt of the resonance
transformer T are in the resonance at first harmonic of the input
voltage Uin.
The output current in "impressed". Its value depends
only on the value of the input voltage Uin and the capacitor C. Due
to this fact , in the application with more secondary windings, the
current distribution depends only on the load impedance and can not
be controlled.
Electrical schema and design parameters
In the Fig 4 are all relevant electrical parameters
of a schema with the resonance transformers. Due to the fact that
the leaking inductance can be included into the impedance Xc and the
inductance L3 into the load impedance the Electrical schema can be
simplified to the schema in the Fig 5.
The parameters in the Fig 5 are calculated as
follows:
ω = 2πf
Xc = L1ω  1/Cω
XL =jLω
Ż = Żload + jL2ω
where f is the main frequency of the input voltage Uin.
Note , if L1 is not big enough to be in
resonance with the capacitor C at a frequency between the 3. and 5.
voltage harmonic then an additional choke has to be used.
Using the first harmonic of the input voltage Uin1
you can calculate:
Uin1 jXL/(jXL
 jXc)=
I (Ż  jXL
jXc/(jXL  jXc))
In the resonance operation mode of
the capacitor C and the main transformer inductance L (Xc = XL) the
load current depends only on the input voltage Uin1 and the capacitor
C: It does not depend on the load impedance. The output current is
constant (impressed) in any operation mode between " noload and "short
circuit". In order to stabile the value of the output voltage you
have to control the input voltage,
I = j Uin1/ Xc
and
Ů = jUin1 Ż/Xc
In a resonance transformer the magnetizing
current is much higher than in a "normal" transformer
and the material investment in the primary winding must be
higher than in the secondary winding. Due to this fact it is
recommended to wind the primary winding "outside", over the
secondary winding.
The main inductance is normally prescribed and it has to be
calibrated using gapped core.
The primary magnetizing current IL can
be calculated as follows:
Uin1 Ż/(Ż  jXc)=
IL (jXL ŻLjXc/(Ż 
jXc))
For the resonance condition Xc = XL
The value for the primary magnetizing current is:
IL = Uin1 Ż/Xc/XL
and
IL = jŮ/XL
= jŮ/Xc
So you can calculate the ratio
between the primary magnetizing current and the primary load current:
IL/I = U/Uin1
Technical specification of the 1200W
resonance transformer
Schema 
Fig. 3 
Frequency 
50kHz 
Nominal output voltage
Nominal output current 
24Vdc
50Adc 


Transformer main inductance L 
0.13 mH (magnetizing current ca.50%) 
Turns ratio W1/W2 
9 
Ambient temperature
Temperature rise
Thermal fuse 
40°C
60°K
120°C 
About the input
Fig. 6
Once again, the output current of the resonance
transformers is "impressed". It has approximately the sine wave
form. The rectifier with the RC load is a nonlinear load. Therefore
the secondary voltage (and the primary voltage too) has the
rectangular for, (Formfac. = 1.00).
The secondary circuit 31 is a good simulation of this
operation mode with rectangular secondary voltage and the sine wave
current.
Due to the fact that you can not prescribe the main
inductance you have to manipulate the size of the gaps in the core
in order to get the prescribed transformer main inductance L =
0.14mH . Gap = 30 means that you will need to sat all 3 gaps in the
ETD core at
approx. 30 x 0.025mm = 0.75mm. Note that the gaps must be calibrated
in order to get the prescribed main inductance 0.13mH.
With PSOrder = 2 primary winding is wound over the
secondary winding because the ampereturns of the primary windings
are ca. 15% bigger.
In order to limit the number of the parallel
connected round wires the eddycurrent factor RacRdc is set to 1.5.
Finally click HERE to
view and print the design results (PDF)
