Power Electronics	
No. 5: Step-down chopper	
with smoothing circuit			Takeshi Furuhashi	
furuhashi_at_cse.nagoya-u.ac.jp		
1Output voltage control	voSW

iovSWEvEVERLvotTonTSW(a) Switching circuit	 TSW(b) Waveform of output voltage	 Switching power supply	 The voltage fluctuation is too large to be used for electroniccircuits.	
2

Voltage vo still fluctuates and 	
there is an inrush current i1
into the capacitor	

Smoothing capacitor	
vL [V]i1

Tr 2SA1015

i1 [mA]ERB
510

C47µF+RL vo400
2000Driving circuit
for Tr	 (a) Switching circuit	 vo76543210i1t [ms]
0

Tr：ON

510OFF	 (b) Waveforms of the output voltage vo and theinput current of capacitor i1	 Switching power supply with smoothing capacitor	 Smoothing is possible not only by capacitor．	
3

The voltage ripple andinrush current aresuppressed. 	

Reactor	 Tr
2SA1015

E6 [V]

RB510

L400µHD

Driving circuit
for Tr	 iL

C47µF

vo [V]+RLvo

Free wheeling diode	 (a) Circuit diagram	 

5iL [mA] 43100250
10000voiL

10

Tr：ON

2030

40t [µs]

OFF	 (b) Waveforms of output voltage vo
and reactor current iL	 

Step-down chopper circuit	 
4Operating principle of the step-down chopper	 
Re1

TrThe power
supply forcesthe current
iLON to flow.

＋	Eｰ	＋	 ｰ	 ＋	L ｰ	iLONvE＋	＋	 +DCｰ	ｰ	RLvo(a) Tr ON	
TrRe2Reactor Lforces thecurrent iLOFF
to flow.

L＋	ｰ	ｰ	 ＋	ｰ	＋	 +iLOFF＋	ｰ	DECRLvo(b) Tr OFF	
Equivalent circuit of the step-down chopper	 

5Re1

VE = 6 [V], Vo = 4.1 [V], L = 400 [µH],Re1= 7 [Ω], fSW = 10 [kHz]	

Li250
L [mA]

iLON

E200

EoVo

150
10050t [ms]0(a) Tr ON	

00.05

0.1

0.150.2

vo [V]
54Re23L21iLOFF

Eot [ms]

0V

00.05

0.1

0.15

0.2o(b) Tr OFF	6

i250
L [mA]iL [mA]

200200

150

150

100
50

100t [ms]000.05

0.1

0.15

0.2

5000

vo [V]

vo [V]

5544332211t [ms]000.050.10.15(a)	 Switching frequency	 

0.10.150.2t [ms]

000.2

0.05

t [ms]

0.05

0.1

0.15

0.2

(b) fSW = 50 [kHz]fSW = 10 [kHz]Waveforms of reactor current iL and output voltage vo	 7

iL [mA]
200
150
10050t [ms]000.050.1

0.15

0.2Expansion of time axis	
iLApproximation
by straight lines	

iLOFF

iLON

Tr：ON	 	 	 	 OFFReactor current iL	 =	tResistance in thecircuit is negligible.	
8vLTr

EVEvLLVE - VoiLON

EotVVooiL(a) Tr ON	 iLONiLOFFvLLiLOFFtEoVo(b) Tr OFF	 

Tr：ON	 	 	 OFF	 

Waveforms of voltage across reactor Land reactor current iL.	 
9

STEP 4. Circuit construction practiceConstruct a motor control circuit.
Control the motor speed by changing the voltage v1. After rotating the motor at a low
speed for a few minutes, check the temperature of the transistor by touching it. Be
careful not to burn your finger.

6V
R2

R2 5102.2k

Tr2SC2120v1	10

Operating region of the transistor in an A-class amplifier	

ICIBVCEVBECollector	 current	 IC [mA]Amplifier using an NPN-type transistor	 Common emitter	VCE [V]Collector-Emitter	 voltage	 
11

STEP 4. problem 1 The circuits below are equivalent circuits in the casewhere Tr is ON and OFF, respectively. The switching frequency oftransistor Tr is high enough that resistance components in the circuits arenegligible. Answer the following questions.	 
(a) Write the differential
equations in the case of
Tr-ON/OFF, respectively.
(b) Assuming that current iLON
= I1 at t = t1, iLON = I2 at t =t2, iLOFF = I2 at t = t2, andiLOFF = I1 at t = t1 + TSW,
solve the differential
equations.
(c) From the solutions in (b),derive two expressions ofthe relationship between
I2 - I1 and duty ratio δ andswitching period TSW.
(d) Derive the relation
between output voltage Voand source voltage VE.	

vLTrELiLON

VEvL
VE - VoEoVotVo(a) Tr ON	 iLvLL
iLOFF

iLON

I2

iLOFF

I1EoVoI1

Tr: ON(b) Tr OFF	 tt2t1	 	 	 	 OFF	 TonTSW12