Download This document gives the RMS and average values of some of the

This document gives the RMS and average values of some of the current waveforms
commonly found in switching power converters. These can be used to calculate the
conduction losses in power semiconductors, capacitors and transformer windings.
In all cases here, the parameter k represents the ratio of ta/T shown in the waveform
diagrams. All the waveforms are time periodic representing constant frequency operation.
T
T
All equations are calculated using I RMS
1
1 2
t

I (t )dt , I AVE   I (t )dt and k  a

T
T0
T0
Trapezoidal Current
The trapezoidal current waveform is commonly found in diodes and active semiconductor
switches for power converters running in continuous conduction mode.
I
Ir
Ia
ta
T
t
Figure 1 – Trapezoidal Current Waveform
For the trapezoidal waveform in Figure 1, the average and RMS values are:-
I 

I AVE  k  I a  r 
2



I2
I RMS  k  I a2  r  I a I r 
3


Equation 1
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Triangular Current
The triangular current waveform shown in Figure 2 is commonly found in power
semiconductors and transformer windings for power converters running in discontinuous
mode.
I
Ia
ta
T
t
Figure 2 – Triangular Current Waveform
For the triangular current waveform in Figure 2, the average and RMS values are:I AVE 
1
Iak
2
I RMS  I a
k
3
Equation 2
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Inductive Current
For a power converter running in continuous conduction mode, the current flowing in the
main power inductor often takes the form as shown in Figure 3.
I
Ir
Ia
ta
t
T
Figure 3 – Inductive Current Waveform
For the inductive current in Figure 3, the average and RMS values are:-
I AVE  I a
I RMS  I a2 
I r2
12
Equation 3
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Offset Trapezoidal Current
The offset trapezoidal current shown in Figure 4 is often found flowing in capacitors for
power stages running in continuous conduction mode.
I
Ir
Ia
Ib
ta
T
t
Note that Ib is a negative number
Figure 4 – Offset Trapezoidal Current
For the offset trapezoidal current shown in Figure 4, the average and RMS values are:-
1 

I AVE  k  I a  I r   I b 1  k 
2 



I2
I RMS  I b2 1  k   k  I a2  r  I a I r 
3


Equation 4
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Offset Triangular Current
The offset triangular current waveform shown in Figure 5 is often found flowing in capacitors
for power converters running in discontinuous conduction mode.
I
Ia
t
Ib
t
T Note that I
b
is a negative number
a
Figure 5 – Offset Triangular Current
For the offset triangular current shown in Figure 5, the average and RMS values are:-
I AVE 
1
kIa  I b
2

I2 
I RMS  I b2  k  I a I b  a 
3

Equation 5
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