Analysis of Output Characteristics of Buck Converter

doi:10.4236/epe.2013.54B203

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Energy and Power Engineering, 2013, 5, 1069-1071

doi:10.4236/epe.2013.54B203 Published Online July 2013 (http://www.scirp.org/journal/epe)

Analysis of Output Characteristics of Buck Converter

Jinquan Wang, Qian Li, Pengchao Song, Pengfei Hou

Engineering Institute of Defence, PLA University of Science&Technology, Nanjing, China

Email: [email protected]

Received February, 2013

ABSTRACT

This Article introduced the concept, topology and function of voltage type Buck converter, built a small signal model,

analysis the negative impedance character of converter, then simulated a Buck-type DC/ DC through MATLAB, ob-

served the dynamic response of converter to pulse-type power load, verified the small-signal theoretical by simulation,

lay the foundation for analyzing DC system stability.

Keywords: Small-signal Model; Nput Impedance; Buck Converter; DC System

1. Introduction

With the rapid development of power electronics tech-

nology and electricity, the number of electronic devices

has more and more extensive application in the grid.

Such a wide range of applications also causing a series of

bad effects, For example, switching tube frequent break-

ing reduces the energy utilization efficiency and lifetime

of the device, the improper design of the internal pa-

rameters of the commutation device will also bring a lot

of problem such as convergence and stability of the sys-

tem[1-3]; Furthermore, the power electronic devices as a

non-linear load inject to grid, resulting in a large number

of harmonics current, which brings a lot of security

problems caused by heat stress. Traditional linear load

statistics matching criteria in this environment has been

challenged. Unstability caused by this power mismatch is

also the key issue of smart micro-grid system, which

consists of source converter output impedance and the

input impedance of the load converter joint decision, in

order to a more convenience study, there need establish

an approximate mathematical model[2,4,5], taking into

account the constant power characteristics of the Buck

converter, there is a negative input impedance character-

istics, according to a given Buck converter, change its

load characteristics, and then separately to analyze the

change in the impedance of the converter. Now study on

DC/DC converter’s negative impedance is mainly con-

centrated in the topology, internal parameters and control

model, in this paper, change the output power to research

Buck circuit input impedance characteristics.

2. Design and Analysis of Voltage type Buck

Converter

2.1. Analysis of Voltage Type Buck

The Buck Chopper is the most widely used form of a

circuit in the DC chopper circuit. Buck circuit is used to

reducing the voltage of the DC power supply, it uses

full-controlled device to control the DC source such of

IGBT, MOSFET and so on, when closed, the DC power

supply to the load, When turned off, the inductor has

been charged still conduct through diode, supply power

to load, so as to achieve the purpose of the step-down

chopper. Having inferred to the following formulation:

EDU



(1)

E－input DC voltage

D－duty

Uo－output voltage

In order to stabilize and adjust the output voltage of

the DC/DC converter, generally, use the voltage or cur-

rent- control mode to adjust the duty cycle, as shown in

Figures 1 and 2. Advantages of current mode control:

faster transient response and improve the stability of the

output voltage accuracy, and has current limiting func-

tion by itself, easy-to-achieve converter overcurrent pro-

tection, and thus easier for multiple power supplies in

parallel achieve both streams. Voltage mode control: the

advantages of detecting only one variable output voltage,

and only one control loop, relatively simple to design and

analysis; due to the large amplitude of the serrasoid

waveform, having the strong anti-jamming capability.

This article only analysis the Voltage type Buck con-

verter.

Uin

-Iref

iLi

PWM

Figure 1. Current type Buck converter.

J. Q. WANG ET AL.

1070

Figure 2 .Voltage type Buck converter.

For a more intuitive understanding of the negative im-

pedance characteristics of the Buck converter, we assume

that the BUCK circuit components are ideal, the power

transfer efficiency of 100%, the converter has been at the

CCM model. The converters simulation can infer that

inductance is smaller, the greater the overshoot, more

stable; capacitance is smaller, smaller overshoot, the

greater the ripple. Therefore there is need to calculate the

appropriate filter capacitors, inductors which can meet

the requirements of the simulation waveform.

For a more intuitive understanding of the negative im-

pedance characteristics of the Buck converter, we assume

that the BUCK circuit components are ideal, the power

transfer efficiency of 100%, the converter has been at the

CCM model. The converters simulation can infer that

inductance is smaller, the greater the overshoot, more

stable; capacitance is smaller, smaller overshoot, the

greater the ripple. Therefore there is need to calculate the

appropriate filter capacitors, inductors which can meet

the requirements of the simulation waveform.

2.2. Small Signal Model

The main course to analysis DC power converter is state

space averaging method [6], given the coefficient matrix

of the equation of state A1, b1, A2, b2, C1

T, C2

T under two

switching state, can infer the mathematical expressions

that describe the steady-state and dynamic small signal

characteristics, induce to the low-frequency equivalent

mode, then through to the disturbance, linearization and

other steps, can get low-frequency small-signal behavior

equation:

12 12

[()() ]

dx ^

xbvAAXb bVd

dt   (2)

()

TTT

yCxC CXd

(3)

By the formula (2) and (3) dynamic low-frequency re-

sponse can be obtained by the Laplace transform of the

small signal characteristics, such as the output of the in-

put to the conduction ratio control transfer function. De-

duced from the voltage on the conduction the transfer

function Gvd ratio control is as follows:

12 12

()0

() ()[( )()

()

ys CsIAA AXbbV

CCX





 



(4)

Transfer function can be obtained from the above equ-

ation:

111 1

vd s

CL D

SCLS

RC LCR



 

(5)

3. Analysis and Simulation

For deep understanding of the closed-loop input imped-

ance characteristics of the converter, establish volt-

age-mode control of the synchronous rectifier BUCK

converter model [7-9] and simulation, as shown in Fig-

ure 3;assuming the efficiency of the inverter is 100%:

0in in

PUI



(6)

In formula Uin and Iin is input voltage and input current.

Small signal perturbations superimposed on the amount

of the steady state in the above formula, get following

formula:

0()(

inin in in

PPUuI i 

)

(7)

Assuming the converter's output power is constant,

that is to ignore the disturbance of the output power:

^^^

0in inininininin in

PUI UiIuui (8)

According to formula (6),then ignores the second or-

der component:

in in



 (9)

The formula (9) explaining the reasons for a

closed-loop input impedance appears the negative resis-

tance characteristic. Absolute of input impedance de-

pending on the size of the input voltage and output power,

make input voltage constant, the converter’s input cur-

rent will be reduced when increasing the output power of

the converter, and verify by simulation following.

Figure 3. Buck converter small signal model.

J. Q. WANG ET AL.

1071

Figure 4. Simulation model.

Figure 5. Current waveform.

In Buck converter simulation, set the voltage feedback

loop control system, the converter input voltage E = 200

V, output voltage Uo = 120 V, the initial resistive load is

1.5 Ω, due to it is assumed that the converter has been

working in CCM state[10-12], according to inductance

L、C of formula, it can obtain the value of the L, C, and

then multiplied by a certain margin coefficient, and fi-

nally set L = 6e-5 H, C = 5e-4F,make simulation time is

0.02 seconds, and paralle a plurality of resistive load in

the load terminal, then trigger pulse at different times, the

purpose of increasing the load is to observe the change of

the input current, and the validation of the negative im-

pedance characteristics. The simulation model is shown

in Figure 4.

4. Results of Simulation

Since the input voltage is maintained at 200 V, only ob-

serve the input current, the increase resistive load added

in 0.002 s, 0.005 s, 0.01 s, taking into account the effi-

ciency of the inverter is 100%, The obtained current

waveform is shown in Figure 5.

Seen by the waveform diagram of the current in the

load side of the power increase, the average of the input

current increases, the input voltage to maintain the same

circumstances, and seen by the Ohm’s law, the input re-

sistance of the converter decreases, showing negative

impedance characteristics.

5. Results of Simulation

It get the same conclusion whether in theoretical way or

simulation way, the voltage Buck converter exhibit nega-

tive impedance characteristics. In order to avoid the ad-

erse effects of the negative impedance characteristics in

engineering, They often put filter in the converter pre-

ceding, increasing the positive impedance to counteract

the negative impedance converter produced, It lead us to

use Buck converter input impedance characteristics to the

next research, such as provides a good reference for

study on DC bus stability.

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