1. Power Converter’s Discontinuous Current Mode Operation
Power PSoC 120:
Power Converter’s Discontinuous Current Mode Operation
Welcome to the CYU’s course on power converters. In this tutorial, we will talk about the discontinuous current mode of operation in power converters and its advantages and disadvantages.

2. Section 1: Introduction
Course Outline
Section 1: Introduction
Section 2: Origin of discontinuous conduction mode
Section 3: Analysis of voltage conversion ratios
This course is divided into 3 sections.

3. At the end of this course, you should be able to:
Course Objectives
At the end of this course, you should be able to:
Understand what discontinuous conduction mode is
Understand how properties of converters change when
this mode is entered
Understand the techniques for solution of the converter waveforms and output voltage
Associated with this course are four main objectives. At the end, you should be able to:
Understand what discontinuous conduction mode is
Understand how properties of converters change when this mode is entered
Understand the techniques for solution of the converter waveforms and output voltage

4. 1
Introduction

5. Properties of converters radically change in DCM
Introduction
Discontinuous Conduction Mode (DCM) is commonly observed in DC-DC converters
DCM arises when the inductor current reduces to zero and tries to reverse
Properties of converters radically change in DCM
Conversion ratio becomes load dependent and load voltage regulation becomes inadequate
The discontinuous conduction mode or DCM typically is observed in DC-DC converters. It is also seen in inverters or in converters containing two-quadrant switches. DCM arises when the inductor current in a switching regulator reduces to zero and tries to reverse. It cannot do so because of the configuration of switches.
The DCM mode typically occurs with large inductor current ripple in a converter operating at light load and containing current-unidirectional switches like MOSFETs and diodes. The properties of converters such as conversion ratio, output impedance change in this mode of operation. The converter dynamics also change significantly. Further the load voltage regulation becomes inadequate.
In this CYU module, we will explain the origin of discontinuous conduction mode and derive the mode boundary. We will consider the buck converter as an example to understand the techniques for solution of converter waveforms and output voltage. We will observe the principles of inductor volt-sec balance and capacitor charge balance must always be true in steady state irrespective of the operating mode.
Doing a small ripple approximation requires care since the inductor current ripple or capacitor voltage ripple is not small compared to the average output current or output voltage. 5

6. 2 Origin of discontinuous conduction mode
In this section, we will see what amounts to a circuit parasitic and how these circuit parasitics contribute to power losses in converters.
Power Converter Circuit Elements

7. Origin of DCM
Let us use the buck converter as a simple example to understand how the inductor and switch current waveforms change as the load power is reduced. The inductor current and diode current waveforms are shown for continuous conduction mode. The inductor current waveform contains a DC component I, plus the switching ripple of peak amplitude iL. During the second interval, the diode current is identical with the inductor current. The inductor current DC component I is equal to the load current I =V/R, since no DC current flows through the capacitor C.
The ripple current magnitude depends on the input and the output voltages, on the inductance L and on the switch conduction time DTS . It does not depend on the load resistance R.
Suppose now the load resistance R is increased, so the DC load current is reduced. The DC component of the inductor current will decrease, but the ripple magnitude iLwill remain unchanged. 7

8. Origin of DCM
If we continue to increase R, a point will be reached where I = iL. It can be seen that the inductor current iL(t) and the diode current iD(t) are both zero at the end of the switching period.
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We will see what happens if we continue to increase the load resistance R. The diode current cannot be negative; therefore, the diode must become reverse biased before the end of the switching period. Now there are three subintervals during each switching period. At the end of the second subinterval during which the diode conducts, the diode current reaches zero and for remainder of the switching period, neither the switch conducts nor the diode conducts. The converter then operates in the discontinuous conduction mode. 8

9. CCM:I > iL DCM:I < iL I > iL Boundary conditions
It can be seen from the buck converter example the diode current is positive as over the entire interval DTS<t<TS provided that I > iL. Therefore the conditions for operation in the continuous and discontinuous conduction modes are:
CCM:I > iL
DCM:I < iL
We know that I=Vo/R = DVi/R and iL= (Vi-Vo)DTS/2L. For DCM, I < iL and therefore by simplification 2L/RTS < (1-D). 9

10. Boundary conditions
Now let K = 2L/RTS and Kcr = D’. The dimension less parameter K is a measure of the tendency of a converter to operate in the discontinuous conduction mode. Large values of K lead to the CCM, while small values lead to DCM. The critical value of K at the boundary of CCM and DCM is a function of the duty cycle and is equal to D’ of the buck converter.
The critical value of Kcr is plotted against the duty cycle D of the buck converter. It is easy to express the boundary conditions in terms of the load resistance R. Rearranging the equations for DCM, we find Rcr=2L/D’TS. So the converter enters the DCM when the load resistance is greater than the critical value Rcr. This critical value depends on the inductance, the switching period, and the duty cycle. Since D’ is less than or equal to 1, the minimum value of Rcr for given circuit conditions is 2L/TS. Therefore, if R<2L/TS, then the converter will operate in the continuous conduction mode for all duty cycles. 10

11. 3
Analysis of voltage conversion ratios
Operating Principle

12. Conversion Ratio
Let us analyze the conversion ratio for the buck converter operating in discontinuous conduction mode. When the switch is on during the time D1Ts, the inductor rises and the converter circuit reduces to the network as shown.
When the switch is off, the inductor current freewheels through the diode during the time D2Ts. During the time D3Ts, neither the switch nor the diode conducts. The corresponding equivalent networks are as shown. 12

13. Inductor volt-sec and capacitor charge balance still hold
Conversion Ratio
Inductor volt-sec and capacitor charge balance still hold
The principles of inductor volt-sec balance and capacitor charge balance still are true for any converter circuit that operates in steady state irrespective of the operating mode.
Further regardless of the operating mode, the capacitor voltage ripple compared to the output voltage magnitude should be small. So the small ripple approximation applies to the output voltage waveform. But for the inductor current, the ripple is not small and is comparable to the output current. Neglecting the inductor current leads to inaccurate results.
The capacitor current and inductor voltage are given against each circuit state. Note the capacitor voltage ripple has been neglected but the inductor current ripple is not neglected. The diode becomes reverse biased at time t = (D1 + D2)Ts. The inductor voltage and inductor current are both zero for the rest of the switching period. 13

14. Inductor volt-sec balance
Conversion Ratio
Inductor volt-sec balance
The average inductor voltage in a switching period must equal zero. Solving for V, we get V= VinD1/(D1+D2). 14

15. Capacitor charge balance
Conversion Ratio
Capacitor charge balance
Similarly the capacitor charge balance must also be satisfied. This implies the average inductor current should be equal to the load current. The average of inductor current is the area of the inductor current triangle; that is half the inductor peak current times the time (D1+D2)Ts.
Now we have two unknowns Vo and D2 with two equations from the inductor current balance and capacitor charge balance equations. Eliminating of D2 from the equations, we have the following equation.
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This output voltage – input voltage relationship equation is valid for K<Kcrs but when K>Kcr the traditional Vo=Dvin holds good. 15

16. Conversion Ratio
The characteristics are plotted here for several values of K. The one thing to note here is that, the effect of the DCM is to cause the output voltage to increase as K falls far below Kcr. 16

17. Course Summary Explained what a DCM is
Parasitics contribute to power losses in converters
Analyzed the conversion ratio for the buck converter in DCM
In Summary, we explained what a discontinuous conduction mode is, showed how circuit parasitics contribute to power losses in converters and analyzed the conversion ratio for the buck converter operating in discontinuous conduction mode.

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