Harmonic Generator Xuanwei Zhu1, Buping Jin2, and Huibin Qin1

1Electronic University Of Science and Technology Of Hangzhou, Hangzhou, China 2Zhejiang Institute of Media and Communications, Hangzhou, China

Emails: zhu19870106@163.com, xxxjbp@126.com, and qhb@hdu.edu.cn

Abstract—With the development of a frequency’s synthesis technology and high speed large-scale integrated circuit, especially the high-speed development of operational amplifier, as a kind of important instrument, the signal generator has a wide range of applications in communication, detection, navigation, and the power supply, etc. It especially has deep applications in the switch power supply. Professor Ruan puts forward a solution—without the electrolytic capacitor harmonic injection method. The harmonic generator has a pivotal role in the aspect of switching power supply, and especially has a particularly evident effect in an odd harmonic. In this paper, we regard the city electricity sampling point between resistances as a benchmark, and the three harmonic is realized with hardware and software, respectively. In the hardware, we use the multiplier and phase-locked loop two methods produce the three times harmonics, and use saber software to simulate the multiplier to ensure the accuracy of the hardware. In the software, we use TMS320F2812 for sine wave generation to realize three harmonic.

Keywords—harmonic injection method; harmonic generator; switching power supply; the simulation software of Saber

I. INTRODUCTION With the development of the science technology,

electronic products are toward miniaturization and intelligence development. The power supply is the electronic product power supply, and the power supply quality and life determines the quality and service life of electronic products. The volume of the power source occupies a bulk volume of electronic products so therefore, engineers are trying various devices to decrease the volume of the power source [2], and replace it with the electrolytic capacitor with CBB capacitor. Professor Xinbo Ruan presented that the harmonic injection method can reduce electrolytic capacitor capacity, in medium and small power switch power sources, and the harmonic injection method, to a certain extent, can reduce the volume of power, but sacrifices the PF value for the price [1]. Therefore, the harmonic generation is a problem for the non-electrolytic capacitors inside. This paper uses two methods of hardware and software to generate three harmonics. The waveform is the harmonic plus resistance sampling sine wave phase as the benchmark, and the output waveform of the differential amplifiers

inside the waveform and the chip multiply, which control each cycle of the peak current of MOSFET tube, making the input current change follow the input voltage, and the PF (power factor) as close to 1.

II. HARDWARE REALIZATION METHOD

A. Application of Multiplier Produces the Three Harmonic.

The mathematical expression of the three harmonic: (t)=A*sin(3* *t)y ω (1)

where A is the amplitude, ω is the angular frequency.

Tπ

ω2

= (2)

In mathematical inside: ttt ωωω 3sin4sin33sin −= (3)

So we need only two multipliers to achieve tω3sin , and after a subtraction circuit we can produce three harmonic. The concrete circuit diagram is shown in Figure 1, where

|sin| tkv aa ω⋅= , |sin| tkv bb ω⋅= . After the two multiplication

av obtain 3av , and

finally the sub tractor output voltage is 33 |sin||sin| tktkv abr ωω ⋅−⋅= (4)

By Formula (3), as long as the ratio of the amplitude of

bv and 3av amplitude (that is

bk and 3ak ) is 3:4,

then rv is a three harmonic.

Figure 1. Generation principle of the three harmonic

Three time harmonic generator performance is mainly by the multiplier, and the following two principle charts show, as Figures 2 and 3.

Figure (2) analog multiplier circuit diagram

A brief introduction of one of its working principles, Figure 2 shows:

4321 bebebebe vvvv +=+ (5) With respect to transistor work in amplification state

[4],, the base emitter voltage and collector have a current accurate logarithmic relationship, and that is:

)ln(s

cTbe i

ivv ⋅= (6)

where Tv is a triode temperature voltage equivalent,

si is the triode reverse saturation current. Hypothesis four triodes are identical (that is Tv equal with

si ), according to the formula (1.2) we have:

4321 cccc iiii ⋅=⋅ (7)

421 3 Rv

Rv

Rv

Rv pzyx ⋅=⋅ (8)

Assume 1R = 2R = 3R = 4R , and make zv equal to 1, then Equation (8) is a variable for:

z

yxp v

vvv

⋅= (9)

Therefore, the circuit realizes multiplication. Figure 3 specific work intention is not introduced here one by one and the idea is similar to Figure 2, and left to the reader to analyze slowly.

Figure 3. With regulating function of analog multiplier circuit diagram

B. Using a Phase Locked Loop Generates Three Harmonic

Phase locked loop is mainly composed of three parts by the phase comparator (PC), the voltage controlled

oscillator (VCO), a low pass filter, as in Figure 4 shows:

Low-pass filter

VCOPhase comparator

Ui Uo

Ud

Figure 4. PLL principle diagram

Figure 5. CD4046 internal circuit principle diagram

Working schematic of CD4046: after input from the 14-pin, the input signal is amplified by the amplifier A1, and reformed; lastly, add to input pins of the phase comparator I and II, the switch K of Figure 3 dial to the 2-pin, so the comparator signals

0U which input from 3-pin compare with input signal

iU as phase in comparator I. The error voltage

ψU of the output from

the phase comparator reflect both the phase difference. By R3, R4 and filtered C2

ψU receive a control voltage

dU , then add to the 9-pin of input port of voltage controlled oscillator, and finally adjust the oscillation frequency F2 of the VCO, make F2 approach the signal frequency f1 quickly. After passing the divider, the output of the VCO input a phase comparator I, then continue to compare phase with theiU , and finally make F2=F1. Both the phase difference

to a certain value, realize the phase locking. If the switch K dials to 13-pin, then the phase comparator II works, and it is the same to the process of the above, no longer burdensome. So as long N equals 3 in Figure 5, then achieve three times multiplier [3]. This is the schematic of the phase locked loop generating frequency multiplication circuit.

10K

R1

10KR2

10K

R3

10KR4

10K

R5

10KR6

10KR7

10k

GND

VCC

VSS

Q1

NPN

Q2

NPN

Q3

NPN

Q4

NPN

GND

VCC

VSS

D1

D2

D3

D4

GND

GND

VCC

VSS

GND

GND

VCC

VSS

1_2

+3

411

*ALM348_A

7_6

+5

411

*BLM348_A

8_9

+10

411

*CLM348_A

14_13

+12

411

*DLM348_A

Vr

Vx

Vy

Vz

III. SOFTWARE REALIZATION Harmonics of general discussion is sine wave, just

the frequency of harmonics are multiples relationship with mains frequencies. So we do harmonic generator, and also do sine wave generator. We can go through the chip of digital signal processing to do control chip of sine wave generator; this paper introduces the use TMS320F2812 [6]-[7] to do sine wave generator briefly.

A. Study on Sine Wave Generator Generally speaking, there are two methods you can

use to generate sine wave. The first method is to use the common look-up table method; it has the advantage of speed, and the FM phase-modulation is easy. If the storage space is large enough, you can get higher accuracy by creating a large lookup table. The second method is a Taylor series expansion method; this method can determine the sine value and cosine value of an angle more accurately, and frequency modulation phase modulations are easy, so this article realizes sine wave signal by the Taylor series expansion method, and sine-sine function of the sine and the cosine function of the algorithm of producing sine wave can expand Tai lei series; the equation is:

...!9!7!5!3

)sin(9753

−+−+−=xxxxxx

...!8!6!4!2

1)cos(8642

−+−+−=xxxxx

Take the first five items of the Taylor series, and obtain the approximate calculation formula:

!9!7!5!3sin

9753 xxxxxx +−+−=

Recursive formula:

sin (nx)=2cos(x)sin[(n-1)x]-sin[(n-2)x],

cos(nx)=2cos(x)sin[(n-1)x]-cos[(n-2)x] By the recursive formula we can see that when we

calculate the sine and cosine values, we need know cos(x) , sin(n-1)x , sin(n-2)x and cos(n-2)x .

B. Software Design This system software can be in accordance with the

idea of modular design to writing, including the main program, constant calculation procedures, duty ratio, calculation program and some corresponding function

subroutine. The main program is used to call the subroutine, to initialize variables, to inquiry keyboard, and to judge whether data needs to refresh, while judging a pulse sent or not and so on. Figure 6 shows the flowchart. In the process, it should calculates duty ratio in the N-1 pulse cycle, and output waveform in the N pulse cycle, which requires completing the calculation in the design to a pulse period. If choosing 20MHz crystal, it only needs 50ns executing of an execution in one octave. If the frequency of output sine wave is 400Hz,where every cycle (2.5ms) needs output 200 pulse; that is to say, a pulse needs 12.5 µ s (equivalent to 12500/50=250 instruction). While executing the calculation program of a duty ratio we only need a few tens of instruction, and this algorithm consider can be achieved from the software overhead.

The main program subroutine began circulating

Determine whether 20 ms?

Determine whether 0.1S?

Refresh display output registers, odd frequency display, even

displaying amplitude

Determining the pulse issued flag register =1?

Clear pulse issued a flag register, regulating duty ratio of

calculation program

Determine whether this procedure is called in the delay

procedure

Return

N

Y

Y

N

N

Y

Y

Y

Figure 6. The main program flow chart

IV. SIMULATION AND ACTUAL CIRCUIT ANALYSIS This paper adopts Saber simulation software to

simulate the multiplier circuit, Figure 7 is the

))))((((98

176

154

132

12222

×−

×−

×−

×−=

xxxxx

)))(((87

165

143

12

1

!8!6!4!21)cos(

2222

8642

×−

×−

×−−=

+−+−=

xxxx

xxxxx

simulation of the circuit diagram. The simulation chip uses LM348, and LM348 itself has four operational amplifiers, and coincides with four operational amplifier conditions implementing multiplier. LM348 is a dual power supply, so we must add 15V power in the simulation and real-time. In the simulation, first it needs to analyze DC operating point for the circuit diagram, so that provides a first operating point for the following analysis.

Figure 7. The simulation of the circuit diagram

The experimental conditions are shown in Table 1.

TABLE 1. SIMULATION CONDITIONS

Amplitude Frequency Type of the Wave Vx 2 50 Sine wave Vy 2 50 Sine wave Vz 1 None DC

Simulation waveform diagram as shown in Figure 8:

Figure 8. Simulation results

Through the simulation results, we can see that the output results of the multiplier relate to two input, and this relation just is the result of the two value multiplied, so the method is right, the following post several physical map:

From the diagram, it can be seen that the simulation

results and real object are consistent so the method is feasible.

V. CONCLUSION Through this experiment, we understand the basic

form the operational amplifier, how to work and some attention of working. We also got a general idea of the hardware structure of TMS320F2812, and learned DSP programming ideas. Through circuit simulation, we learned concrete operation of Saber simulation software in the simulation; we also encountered many problems, and solved the problems one-by-one through the Internet to find information. Through the analysis of LM348 operational amplifier, we know that a triode generally works in the enlarged area. Only guarantee triode working in amplification to ensure consistent results, in order to increase the anti-jamming ability, we generally should add a filter capacitor in the VCC and the input port.

REFERENCE [1] X. Ruan. “Means of eliminating electrolytic capacitor in

AC/DC power supplies for LED lightings,” IEEE Transaction on Power Electronics, vol. 24, no. 5, May 2009.

[2] C. Qiao, and K. M. Smedley. “A topology survey of single-stage power factor correction with a boost type input-current-shaper,” in Proc. IEEE APEC 2000, pp. 460-467.

[3] Y. K. Lo, S. C. Yen, and J. Y. Lin. “A high-efficiency AC-to-DC adaptor with a low standby power consumption,” in Proc. IEEE PESC 2006, pp. 18-22.

[4] S. Tong. Fundamentals of analog electronic technology (fourth edition). Beijing: Higher Education Press, 2001.

[5] W. Gu. Taught you how to learn DSP: Based on TMS320X281x. Bei Hang University, 2011

[6] TMS320F281x Datasheet. Texas Instruments, 2003.