I. Series Resonant Converter:

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ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
Resonant converters are used to reduce/eliminate the switching losses. There are three basic
types of the resonant DC/DC converters:
1. Series resonant converter
2. Parallel resonant converter
3. Series-Parallel resonant converter
I.
Series Resonant Converter:
S1
S2
D1
+
D2
Vi
_
S4
S3
D4
is
L
C
Dr1
N1: N2
+
+
vs
_
vp
_
+
vsec
_
ior
Io
Co
RL
+
Vo
_
Dr2
D3
Figure 1
One method of controlling the output voltage in resonant converters is to control the switching
frequency of the full-bridge inverter. This method is called ‘variable frequency control’. In this type
of control, the switching frequency (fs) controls the impedance of the resonant components connected
between the inverter and the load. This in-turn controls the power flow from the input to the output
and, therefore, the output voltage. The resonant components L and C have a fixed value of the
resonant frequency ( f r  1
2
LC ). Depending upon the value of the frequency, the converter operates
in the following three modes:
1.
2.
3.
Below resonance mode (fs < fr)
Above resonance mode (fs > fr)
At resonance mode (fs = fr)
In the below resonance mode, the switching frequency of the converter is lower than the resonant
frequency. While in the above resonance mode, the switching frequency of the converter is higher
than the resonant frequency. Obviously, at the resonance mode, both the frequencies are equal. The
operating waveforms of the converter in these modes are given in Figure 2. In Figure 2, Vg,S1, Vg,S2,
Vg,S3 and Vg,S4 represent the gate signal applied to switch S1, S2, S3 and S4 respectively.
1
ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
Vg,S1
Vg,S3
t
Vg,S2
Vg,S4
vs
t
Vi
t
is
t
vp
t
ior
Io
t
Vo
t
Ts /2
Ts
(a) Below resonance
2
current is leads
voltage vs
ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
Vg,S1
Vg,S3
t
Vg,S2
Vg,S4
vs
t
Vi
t
is
t
vp
t
ior
Io
t
Vo
t
Ts /2
Ts
(b) Above resonance
3
current is lags
voltage vs
ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
Vg,S1
Vg,S3
t
Vg,S2
Vg,S4
vs
t
Vi
t
is
t
current is in phase
with voltage vs
vp
t
ior
Io
t
Vo
t
Ts /2
Ts
(c) At resonance
Figure 2
 Analysis of the Series Converter
Since a resonant circuit is connected between the inverter and the load, it can be assumed that the
current harmonics in the series resonant circuit are very small. Therefore, we are going to consider the
fundamental equivalent circuit only. Also, for the fundamental circuit, the rectifier load at the primary
4
ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
of the transformer can be represented by an equivalent AC resistance Rac  8 RL . The equivalent
2

circuit of the converter of Figure 1 is given in Figure 3.
jωsL
is
-j/ωsC
+
+
vs1
_
vop
_
Rac
Zs
Figure 3
Mathematical Analysis According to the Equivalent Circuit shown in Figure 3:
Since vs is a square voltage waveform, the RMS value of the inverter voltage (vs) is represented by
Vs1 as shown in (1):
Vs1 
2 2

Vi  0.9Vi ------------------------------------------------------

1 

Z s  Rac  j s L 
s C 

-------------------------------------------
(2)
------------------------------------------------------
(3)
v s1 v s1

   -----------------------------------------------------Zs
Zs
(4)
 Z s 
is 
(1)


 s L  1  

 s C  
1  
  tan 

Rac






Defining the following quantities:
s  2f s  operating angular switching frequency
5
[rad/s]
ELEC 431 Class notes
Resonant DC/DC Converters
fs = operating switching frequency
Q
fr 
P.K. Jain
[Hz]
2f r L
1

 Quality factor
Rac
2f r CRac
1
2 LC
 Resonant frequency
[Hz]
r  2f r  Angular resonant frequency
[rad/s]
From equation (2):

 L
1  

Z s  Rac 1  j  s 

R

CR
s
ac  
 ac


  L 
1  

 Rac 1  j  s r  r

  r Rac  s  r CRac  



1  
 Rac 1  j  Q 
Q


  




1
 Rac 1  jQ   





---------------------
(6)




In equation (6),

s
 Relative angular operating frequency
r
Since,
Z s  Z s 
1/ 2
Hence
→
2

1 

Z s  Rac 1  Q 2     

  


-----------------------------------
(7)
→
 
1 
  tan 1  Q     
 
 
-----------------------------------
(8)
The inverter’s output current:
6
ELEC 431 Class notes
Resonant DC/DC Converters
is 
is 
P.K. Jain
Vs1
Z s 
0.9Vi   
2


1


2
Rac 1  Q     

  


1/ 2
-----------------------------------
(9)
1/ 2
----------------------------------
(10)
The magnitude of the output voltage vop is then
vop  is Rac
vop

0.9Vi
2


1  Q 2    1  

  


 The output voltage of the converter can, therefore, be controlled by controlling the relative
operating frequency ω or f. Figure 4 shows the output voltage control as a function of f.
7
ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
vop
0.9vi
Small Q
(a) output voltage
High Q
f= fr / fs
Capacitive impedance
Inductive impedance
|Zs|
ɸ
(b) Impedance
magnitude
f= fr / fs
90°
(c) Impedance
angle
0
f= fr / fs
-90°
1.0
Figure 4
The converter can operate in the following three modes:
1.
f < 1: In this mode fs/fr < 1, and it is called “below resonance mode”.
 In this mode, the impedance seen by the inverter is capacitive. This causes a
“leading” current with respect to the inverter output voltage vs. With the leading
current, the inverter operates with the zero current switching (ZCS).
2. f = 1: In this mode fs/fr = 1, and it is called “At resonance mode”.
 In this mode, the impedance seen by the inverter is resistive. Both the inductive and
capacitive impedances cancel each other. The output current ‘or’ voltage of the
converter is maximum. The inverter output current is in phase with the voltage.
With this the inverter operates with ZCS.
3. f > 1: In this mode fs/fr > 1, and it is called “above resonance mode”.
8
ELEC 431 Class notes
Resonant DC/DC Converters
P.K. Jain
 In this mode, the impedance seen by the inverter is inductive. This causes a
“lagging” current with respect to the inverter output voltage vs. With the lagging
current, the inverter operates with the zero voltage switching (ZVS).
From Figure 4(a), it is clear that the maximum output voltage, therefore, the maximum power is
obtained at the resonance point. The output voltage can be controlled either by reducing the
operating frequency or by increasing the operating frequency. The operation of the converter is,
however, preferred by increasing the frequency because the converter operates with ZVS. ZVS is a
better technique than ZCS because with ZVS, both the turn-on and turn-off losses can be effectively
reduced. In ZCS, only the turn-off loss can be reduced. However, the ZCS technique is preferred
with the switches that rely on the external circuits to commutate. One example of such a switch is
the “thyristor or SCR”.
Advantages of the Series Resonant Circuit:
The main advantage of the series resonant converter is its simplicity and its high efficiency from
full-load to reduced-load.
Disadvantages of the Series Resonant Circuit:
The main drawback of the series resonant circuit is that it loses the output voltage control at very
reduced loads and no loads.
9
ELEC 431 Class notes
II.
Resonant DC/DC Converters
P.K. Jain
Parallel Resonant Converter:
S1
S2
D2
D1
+
Vi
_
L
is
C
vs
_
S3
D4
ior Lo
io
+
vsec
_
+
+
S4
Dr1
N1: N2
vp
_
Co
RL
+
Vo
_
Dr2
D3
Figure 5
Advantage: No-load to full-load possible
Disadvantage: Low efficiency at reduced loads
III.
Series-Parallel Resonant Converter:
S1
S2
D1
+
D2
Vi
_
is
L
Cs
+
+
S4
vs
_
S3
D4
Cp
Dr1
N1: N2
vp
_
Figure 6
Advantage: No-load to full-load possible
Disadvantage: Good efficiency from full-load to reduced-load
10
Lo
Co
+
vsec
_
Dr2
D3
ior
io
RL
+
Vo
_
×

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