Condizioni di commutamento di hard-switching nei convertitori DC/DC

U à S N

niversit degli tudi di apoli

F ederico II

Dipartimento di Ingegneria Elettrica e

delle Tecnologie dell’Informazione

Classe di Laurea in Ingegneria dell’Informazione, Classe n. L.8

Corso di Laurea in Ingegneria Elettronica

Elaborato di Laurea

Hard-Switching behaviour in SMPS: analysis and consideration

Anno Accademico

2017/2018

Appendix A

Switch-mode power converter

compensation

A switch mode power supply regulates the output voltage against any change in the

output loading or in the input line voltage. To accomplish this regulation, a feedback

loop is required. Since the feedback loop requires compensation if it has an error

amplifier with linear feedback, different solutions and compensation techniques may

be used, depending on the topology and characteristics of the power converter.

This section’ aim is to provide an overview of the most common compensation

techniques with a particular focus on the Type II compensation for a boost converter

working in the CCM with a peak current mode control. Although, there are many

techniques to select the compensation component values, the method used for the

project and shown in this section is based upon setting the mid-band gain of the error

amplifier transfer function. To create Bode plot of gain and phase for the power stage

and error amplifier, Matlab software has been used, its code is reported at end of the

section, in order to observe how it changes in compensation or the way the power stage

affects the gain and phase system in.

A.1 Compensation Techniques

The SMPS can work on two different operation modes: CCM and DCM. The

regulation of the output voltage is obtained through a feedback loop which needs to be

compensated since power converter are naturally unstable because of presence of zeros

and poles. The compensation choice depends on the control technique used for the

loop: VMC or CMC as well.

Typically, compensations techniques are divided into three categories or

types: I, II, III compensator type. 90

A.1.1 Type I error amplifier

Figure A.1 shows a Type I error amplifier configuration, which is the simplest form

of compensation. It consists of a single pole and the amplifier is an inverting

configuration with a virtual short between V and V . The feedback impedance

FB REF

divided by the input impedance gives the small signal gain, since the R may be seen

FBB

as an AC ground and it is possible to ignore it because it does not affect the AC transfer

function. Figure A.1 Type I error amplifier compensation [22].

By summing the currents at the error-amplifier inputs, the relation is the following:

1 1

( )

+ = + (1)

Since we are interested in the transfer function, we need to write the feedback voltage

in terms of input or control voltage. It is possible to notice that the feedback voltage

may be related to the control voltage by the open loop gains of the amplifier, in this

way the Eq. 2: −

= (2)

Combining Equations 1 and 2:

1

( )

=− (3)

1

1 + ∙ (1 + )

If the gain of the error amplifier is large enough:

91

( )≫1

(4)

+

Then the closed-loop gain can be expressed as:

≈− =− (5)

Where w defines the error amplifier pole frequency:

EA 1

= (6)

∙

The Equation 6 reveals a single pole at the origin, and it is limited at the DC by the

open-loop gain of the amplifier and it is called dominant-pole compensation. Its

frequency response is depicted in Fig. A.2

Figure A.2 Type I error amplifier compensation [22].

Type I compensation is often used for a constant-current type load, such as a light-

emitting diode (LED) load with no output capacitor. It is also clear that using this

technique for any power supply or systems does not offer the flexibility necessary to

achieve an optimal performance [43]. 92

A.1.2 Type II error amplifier

The schematic of a Type II error amplifier is shown in Fig. A.3.

Figure A.3 Type II error-amplifier compensation [43].

Using the same derivation process as for Type II compensation, the Equation 7

expresses the voltage-gain transfer function:

1 +

≈− (7)

1+

where A is defined as the mid-band voltage gain which results in:

VM

≈ (8)

The voltage-gain transfer function (Eq.7) reveals the presence of a high-frequency pole

at: 1

≈ , ≫ (9)

and a zero at: 1

= (10)

Also, in this case, the open-loop gain of the amplifier will limit the error-amplifier gain

at DC but less compared to Type I. Generally, Type II compensation is well suited for

use with current-mode control [43]. Figure A.3 shows the approximation of the

frequency response of Type II error amplifier.

93

Figure A.4 Frequency response for a Type II error amplifier [43].

A.1.3 Type III error amplifier