Buck ConverterCyril Aloysius A. Quinto

Department of Electrical and Electronics Engineering, University of the Philippines-DilimanDiliman, Quezon City, Philippinesaloysius.quinto@gmail.com

cyrilaloysius.quinto@emerson.com

Abstract— This document describes lab experiment #5 for EE241. This familiarizes one with the characteristics of the buck converter. It also verifies the theoretical computations with the simulated results.

Keywords— Buck, Duty, Discontinuous, Continuous

I. INTRODUCTION

Switched Mode Power Supplies replaced the linear regulators as demand for better efficiency cropped up.

Among the basic topologies are buck, boost, and buck-boost. From these, derived topologies can be obtained to come up with a new one.

The buck topology offers higher efficiencies versus their linear counterparts. This uses energy storing devices such as the inductor and the capacitor. The buck topology produces a stepped down output only.

Two modes of operation are commonly used, namely, continuous and the discontinuous mode.

II. SIMETRIX EXERCISE DESCRIPTION

A. Buck Converter Operation

Probe1-NODE5m

R5200u

C1

47

R4

50m

R2

D1

mbr6045wt

100u

L1

12

V1

Q1

irf 150

5

R1

V2

L1-P

Fig 1. Shows a Buck Circuit Operating at 100kHz.

Build the circuit as shown in Fig 1. V2 is a pulsed generator with 8V amplitude, 4V offset, fs =100kHz, 50% duty.

Plot the switching voltage(Vgs), inductor current (IL), switch current(Ids) and diode current (Id). From these graphs, explain how a buck converter works. Are the graphs consistent with the idealized current and voltage waveforms? Explain any difference. Is it in DCM or CCM?

B. Varying the Duty Cycle

What is the average output voltage?Repeat 2a with varying duty from 20% to 80%, in steps of

10%. What happens to Vo? Is this consistent with the theoretical relationship of Vo and Duty Cycle. Explain any discrepancy.

C. Varying the Switching Frequency

Maintain RL = 5ohms, Fs =100kHz, Set duty to 50%. Measure the peak to peak value of Vo and IL.

Repeat with varying Fs with Vo maintained. Change the duty as frequency is varied: 100kHz: 50%, 80kHz:50.75%, 60kHz:51%, 40kHz:51.6%.

What is the effect on the ripples as you vary the switching frequency?

D. Input Voltage Disturbance Increase Vin to 24V, maintain the Vo to the value in B by varying the duty cycle. Take note of this duty cycle. Decrease Vin to 15V, again maintain the Vo by varying the duty. Note this duty.

E. CCM/DCM Boundary Increase or decrease the load resistor in Fig 1. What happens to the inductor waveform? Measure the inductor current for different values of L1 in Fig 1. Find the value of the inductance which will the converter enter into DCM. You may use multistep transient analysis in approximating the value of boundary inductance.

III. RESULTS AND DISCUSSIONS

A. Buck Converter Operation

Fig 2. Shows Buck Vgs, IL,Ids and Id Initially, Q1 is shown to be ON while D1 is OFF. At this moment, IL is shown to be charging to a peak value given by

(Vin-Vo)Ton/ Lp. At the time when Q1 is off, since an inductor can’t tolerate an instantaneous current change, the voltage across L1 reverses in polarity to keep the current across it flowing. The node connecting Q1, L1 and D1 goes to -0.7V, by then, D1 starts conducting. The downward slope of the current is, then, given to be Vo/Lp = dIs/Toff (if the cut in voltage of the diode is not included). If we overlap all the currents, it will show the current across Lp to just be equivalent to IQ and Id combined.

Fig 3. Shows IQ, Id and IL Overlapping.

Fig 3 also shows the buck to operate in CCM mode as the current in the inductor does not go into zero. The simulated results jibe with what is expected for a buck.

B. Varying the Duty Cycle

The average voltage for the output is given to be 6.369V as shown in Fig 2. Fig 4 shows that, as the duty is increased, Vo is seen to increase. This is consistent with the equation for the buck. Using the equality of the volt-second products for both Ton and Toff, Duty = Vo/Vin. Vo = Duty* Vin, which is consistent with what is shown in Figs 4 and 5. This is consistent with the theoretical relationship of Vo and Vin.

Fig 4. Varying Duty from 20% to 80% in steps of 10%.

Fig 5. Comparison Between 20% and 80% Duty.

C. Varying the Switching Frequency

Fig 6. Shows the Output Voltage and Inductor Current Ripple Fig 6 shows Vopk-pk = 154.52mV and Ilpk-pk = 897.97mA. Theoretically, Vo is expected to be given by Vo = D*Vin.Vo will then be equal to around 6V. Having a 5ohm output resistance means that the Io will be 6V/5ohms = 1.2A.

Vo = D*Vin eqn 1.(Vin-Vo) = LpdIL/Ton eqn 2.Ton = D*T eqn 3.T = 1/fsw eqn 4.

The ripple of the inductor current can be obtained with eqns 2 to 4 combining to result to the equation below:

dIL = (Vin-Vo)*D/(fsw*Lp) eqn 5.

At D = 50%, fsw = 100kHz and RL = 5ohms, dIL = 0.3A. Equation 6 gives the expected Vo ripple:

Vo = ESR * dIL = 50m* 0.3A = 15 mV. Fig 6a verifies the theoretical expectations set by the equations outlined above. It is found to be a little off because of the measurements. Even with cursors employed, the frequency of the ripple was not properly caught. Also, the duty is not necessarily 50%, as the duty is not properly controlled compared if an IC was used, instead. If we zoom in on the waveforms as in Fig 6a, we can see a better correlation between computed and experimental results.

Fig 6a.Close up on IL and Vo ripple.

Fig 7. Shows IL and Vo ripple with Varying Switching Frequencies. Fig 6a shows Vopkpk = 15.01mV and dIL = 302.6mA as predicted by the equations above. Fig 7 shows the Vo and inductor current ripple as frequency is varied. Fig 7a shows the measurements of both inductor current ripple and Vo ripple in decreasing switching frequency.

100kHz 426.1mA 132.5mV 80 kHz 481mA 118mV60 kHz 640.6mA 150.8mV40 kHz 899.1mA 155.4mV

To better observe the results, Vo should be separated and zoomed in to avoid incorrect Vo ripple readings. But the inductor currents show a relative increase in the ripple as the frequency is lowered. Equation 5 reveals that as the switching frequency is increased, the inductor current ripple becomes less. Thus, the Vo ripple is also found to be less as the switching frequency is increased.Fig 7a. Measurements of Inductor Current Ripple

D. Input Voltage Disturbance

Fig 8. Shows Duty as Vin is made 24V.

Fig 9. Shows Duty at Vin = 15V.

Fig 8 shows a duty of around 25% when Vin =24V compared to duty = 50% at Vin 12V. The duty = 39.5% at 15V input. This is consistent with Equation 1 as defined above. The slight difference is attributed to the measurement of the simulator as the transient response on the first 1us is also taken into account for Vo measurements. Equation 1 defines how the duty controls the output voltage for a buck converter. The buck converter regulates the Vo by either increasing or decreasing the duty of Q1. When Vin is increased, to keep the volt-second product of the inductor at both ON and OFF times equal, the duty is decreased. Also, as Vin is lowered, the duty is increased to regulate the output. As the load increases, Vo initially lowers in value. As a response, the buck converter increases in duty. On the other hand, when the load is decreased, Vo tends to increase initially, the buck converter decreases in duty to regulate the output.

This behaviour of the buck can be attributed to the equation Vo= D*Vin.

E. CCM/DCM Boundary

Fig 10. Shows IL as RL is Varied.

Fig 11. Measurements of Inductor Ripple at Varying L1. It can be seen from Fig 10 that at lighter loads(higher RL), the inductor current goes to zero. At lower RL, the inductor current does not go to zero at all. At a much higher RL(around 100 ohms), the current is seen to touch the zero current always. This is the DCM operation. At lower RL, the buck is seen to operate at CCM.

Fig 10a shows the ripple current to vary as L1 is varied:20uH 1.848A40uH 918.3mA60uH 615.7mA80uH 470.9mA100uH 390.2mA

Fig 11a. A Close Up of the Inductor Current at Diff L1 Values.

Fig 12. Shows L1 Values at which the Boundary between CCM and DCM happens.It can be observed that the inductor ripple current reduces

as L1 is increased. This implies that a CCM operation requires a higher inductance, therefore, a larger inductor.

Fig 12 shows that the boundary condition between DCM and CCM with RL = 5ohms happens at L1 = 12uH.

IV. CONCLUSIONS

The buck converter was carefully studied. It was found out that it regulates the output depending on line and load variations by changing its duty. The change in duty is governed by D = Vo/Vin. It was also found out that the inductor ripple current decreases as the switching frequency is increased. This also affects the Vo ripple as Voripple = dIL*ESR. It was also learned that at lighter loads(high RL), it initially operates in DCM. The choice of the inductor value dictates whether it operates in DCM or CCM at a given switching frequency.

It can be concluded that the objectives of this experiment were successfully attained.

REFERENCES

[1] Pressman, Billings and Morey, Switching Power Supply Design, 3rd ed., McGrawHill Companies, USA, 2009.