Sine Wave Generation Techniques - National Semiconductor

Sine Wave Generation

Techniques

Producing and manipulating the sine wave function is a

common problem encountered by circuit designers. Sine

wave circuits pose a significant design challenge because

they represent a constantly controlled linear oscillator. Sine

wave circuitry is required in a number of diverse areas,

including audio testing, calibration equipment, transducer

drives, power conditioning and automatic test equipment

(ATE). Control of frequency, amplitude or distortion level is

often required and all three parameters must be simulta-

neously controlled in many applications.

A number of techniques utilizing both analog and digital

approaches are available for a variety of applications. Each

individual circuit approach has inherent strengths and weak-

nesses which must be matched against any given applica-

tion (see table).

Phase Shift Oscillator

A simple inexpensive amplitude stabilized phase shift sine

wave oscillator which requires one IC package, three tran-

sistors and runs off a single supply appears in Figure 1. Q2,

in combination with the RC network comprises a phase shift

configuration and oscillates at about 12 kHz. The remaining

circuitry provides amplitude stability. The high impedance

output at Q2’s collector is fed to the input of the LM386 via

the 10 µF-1M series network. The 1M resistor in combination

with the internal 50 kΩunit in the LM386 divides Q2’s output

by 20. This is necessary because the LM386 has a fixed gain

of 20. In this manner the amplifier functions as a unity gain

current buffer which will drive an 8Ωload. The positive peaks

at the amplifier output are rectified and stored in the 5 µF

capacitor. This potential is fed to the base of Q3. Q3’s

collector current will vary with the difference between its

base and emitter voltages. Since the emitter voltage is fixed

by the LM313 1.2V reference, Q3 performs a comparison

function and its collector current modulates Q1’s base volt-

age. Q1, an emitter follower, provides servo controlled drive

to the Q2 oscillator. If the emitter of Q2 is opened up and

driven by a control voltage, the amplitude of the circuit output

may be varied. The LM386 output will drive 5V (1.75 Vrms)

peak-to-peak into 8Ωwith about 2% distortion. A ±3V power

supply variation causes less than ±0.1 dB amplitude shift at

the output.

00748301

FIGURE 1. Phase-shift sine wave oscillators combine simplicity with versatility.

This 12 kHz design can deliver 5 Vp-p to the 8Ωload with about 2% distortion.

National Semiconductor

Application Note 263

October 1999

Sine Wave Generation Techniques AN-263

Sine-Wave-Generation Techniques

Typical Typical Typical

Type Frequency Distortion Amplitude Comments

Range (%) Stability

(%)

Phase Shift 10 Hz–1 MHz 1–3 3 (Tighter Simple, inexpensive technique. Easily amplitude servo

with Servo controlled. Resistively tunable over 2:1 range with

Control) little trouble. Good choice for cost-sensitive, moderate-

performance applications. Quick starting and settling.

Wein Bridge 1 Hz–1 MHz 0.01 1 Extremely low distortion. Excellent for high-grade

instrumentation and audio applications. Relatively

difficult to tune — requires dual variable resistor with

good tracking. Take considerable time to settle after

a step change in frequency or amplitude.

LC 1 kHz–10 MHz 1–3 3 Difficult to tune over wide ranges. Higher Q than RC

Negative types. Quick starting and easy to operate in high

Resistance frequency ranges.

Tuning Fork 60 Hz–3 kHz 0.25 0.01 Frequency-stable over wide ranges of temperature and

supply voltage. Relatively unaffected by severe shock

or vibration. Basically untunable.

Crystal 30 kHz–200 MHz 0.1 1 Highest frequency stability. Only slight (ppm) tuning

possible. Fragile.

Triangle- <1 Hz–500 kHz 1–2 1 Wide tuning range possible with quick settling to new

Driven Break- frequency or amplitude.

Point Shaper

Triangle- <1 Hz–500 kHz 0.3 0.25 Wide tuning range possible with quick settling to new

Driven frequency or amplitude. Triangle and square wave also

Logarithmic available. Excellent choice for general-purpose

Shaper requirements needing frequency-sweep capability with

low-distortion output.

DAC-Driven <1 Hz–500 kHz 0.3 0.25 Similar to above but DAC-generated triangle wave

Logarithmic generally easier to amplitude-stabilize or vary. Also,

Shaper DAC can be addressed by counters synchronized to a

master system clock.

ROM-Driven 1 Hz–20 MHz 0.1 0.01 Powerful digital technique that yields fast amplitude

DAC and frequency slewing with little dynamic error. Chief

detriments are requirements for high-speed clock (e.g.,

8-bit DAC requires a clock that is 256 x output sine

wave frequency) and DAC glitching and settling, which

will introduce significant distortion as output

frequency increases.

Low Distortion Oscillation

In many applications the distortion levels of a phase shift

oscillator are unacceptable. Very low distortion levels are

provided by Wein bridge techniques. In a Wein bridge stable

oscillation can only occur if the loop gain is maintained at

unity at the oscillation frequency. In Figure 2a this is

achieved by using the positive temperature coefficient of a

small lamp to regulate gain as the output attempts to vary.

This is a classic technique and has been used by numerous

circuit designers*to achieve low distortion. The smooth

limiting action of the positive temperature coefficient bulb in

combination with the near ideal characteristics of the Wein

network allow very high performance. The photo of Figure 3

shows the output of the circuit of Figure 2a. The upper trace

is the oscillator output. The middle trace is the downward

slope of the waveform shown greatly expanded. The slight

aberration is due to crossover distortion in the FET-input

LF155. This crossover distortion is almost totally responsible

for the sum of the measured 0.01% distortion in this oscilla-

tor. The output of the distortion analyzer is shown in the

bottom trace. In the circuit of Figure 2b, an electronic equiva-

lent of the light bulb is used to control loop gain. The zener

diode determines the output amplitude and the loop time

constant is set by the 1M-2.2 µF combination.

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Low Distortion Oscillation (Continued)

The 2N3819 FET, biased by the voltage across the 2.2 µF

capacitor, is used to control the AC loop gain by shunting the

feedback path. This circuit is more complex than Figure 2a

but offers a way to control the loop time constant while

maintaining distortion performance almost as good as in

Figure 2.

Note: *Including William Hewlett and David Packard who built a few of these

type circuits in a Palo Alto garage about forty years ago.

High Voltage AC Calibrator

Another dimension in sine wave oscillator design is stable

control of amplitude. In this circuit, not only is the amplitude

stabilized by servo control but voltage gain is included within

the servo loop.

A 100 Vrms output stabilized to 0.025% is achieved by the

circuit of Figure 4. Although complex in appearance this

circuit requires just 3 IC packages. Here, a transformer is

used to provide voltage gain within a tightly controlled servo

loop. The LM3900 Norton amplifiers comprise a 1 kHz am-

plitude controllable oscillator. The LH0002 buffer provides

low impedance drive to the LS-52 audio transformer. A volt-

age gain of 100 is achieved by driving the secondary of the

transformer and taking the output from the primary. A

current-sensitive negative absolute value amplifier com-

posed of two amplifiers of an LF347 quad generates a

negative rectified feedback signal. This is compared to the

LM329 DC reference at the third LF347 which amplifies the

difference at a gain of 100. The 10 µF feedback capacitor is

used to set the frequency response of the loop. The output of

this amplifier controls the amplitude of the LM3900 oscillator

thereby closing the loop. As shown the circuit oscillates at 1

kHz with under 0.1% distortion for a 100 Vrms (285 Vp-p)

output. If the summing resistors from the LM329 are re-

placed with a potentiometer the loop is stable for output

settings ranging from 3 Vrms to 190 Vrms (542 Vp-p!) with

no change in frequency. If the DAC1280 D/A converter

shown in dashed lines replaces the LM329 reference, the AC

output voltage can be controlled by the digital code input with

3 digit calibrated accuracy.

00748302

(a)

00748303

(b)

FIGURE 2. A basic Wein bridge design (a) employs a lamp’s positive temperature coefficient

to achieve amplitude stability. A more complex version (b) provides

the same feature with the additional advantage of loop time-constant control.

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High Voltage AC Calibrator (Continued)

00748304

Trace Vertical Horizontal

Top 10V/DIV 10 ms/DIV

Middle 1V/DIV 500 ns/DIV

Bottom 0.5V/DIV 500 ns/DIV

FIGURE 3. Low-distortion output (top trace) is a Wein bridge oscillator feature. The very

low crossover distortion level (middle) results from the LF155’s output stage. A distortion

analyzer’s output signal (bottom) indicates this design’s 0.01% distortion level.

00748305

A1–A3 =

⁄

LM3900

A4 = LH0002

A5–A7 =

⁄

LF347

T1 = UTC LS-52

All diodes = 1N914

* = low-TC, metal-film types

FIGURE 4. Generate high-voltage sine waves using IC-based circuits by driving a transformer in a step-up mode.

You can realize digital amplitude control by replacing the LM329 voltage reference with the DAC1287.

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Negative Resistance Oscillator

All of the preceding circuits rely on RC time constants to

achieve resonance. LC combinations can also be used and

offer good frequency stability, high Q and fast starting.

In Figure 5 a negative resistance configuration is used to

generate the sine wave. The Q1-Q2 pair provides a 15 µA

current source. Q2’s collector current sets Q3’s peak collec-

tor current. The 300 kΩresistor and the Q4-Q5 LM394

matched pair accomplish a voltage-to-current conversion

that decreases Q3’s base current when its collector voltage

rises. This negative resistance characteristic permits oscilla-

tion. The frequency of operation is determined by the LC in

the Q3-Q5 collector line. The LF353 FET amplifier provides

gain and buffering. Power supply dependence is eliminated

by the zener diode and the LF353 unity gain follower. This

circuit starts quickly and distortion is inside 1.5%.

Resonant Element

Oscillator—Tuning Fork

All of the above oscillators rely on combinations of passive

components to achieve resonance at the oscillation fre-

quency. Some circuits utilize inherently resonant elements to

achieve very high frequency stability. In Figure 6 a tuning

fork is used in a feedback loop to achieve a stable 1 kHz

output. Tuning fork oscillators will generate stable low fre-

quency sine outputs under high mechanical shock condi-

tions which would fracture a quartz crystal.

Because of their excellent frequency stability, small size and

low power requirements, they have been used in airborne

applications, remote instrumentation and even watches. The

low frequencies achievable with tuning forks are not avail-

able from crystals. In Figure 6, a 1 kHz fork is used in a

feedback configuration with Q2, one transistor of an LM3045

array. Q1 provides zener drive to the oscillator circuit. The

need for amplitude stabilization is eliminated by allowing the

oscillator to go into limit. This is a conventional technique in

fork oscillator design. Q3 and Q4 provide edge speed-up

and a 5V output for TTL compatibility. Emitter follower Q5 is

used to drive an LC filter which provides a sine wave output.

Figure 7, trace A shows the square wave output while trace

B depicts the sine wave output. The 0.7% distortion in the

sine wave output is shown in trace C, which is the output of

a distortion analyzer.

00748306

FIGURE 5. LC sine wave sources offer high stability and reasonable distortion levels. Transistors Q1 through Q5

implement a negative-resistance amplifier. The LM329, LF353 combination eliminates power-supply dependence.

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Resonant Element Oscillator—Tuning Fork (Continued)

00748307

Q1–Q5 = LM3045 array

Y1 = 1 kHz tuning fork, Fork Standards Inc.

All capacitors in µF

FIGURE 6. Tuning fork based oscillators don’t inherently produce sinusoidal outputs. But when you do use

them for this purpose, you achieve maximum stability when the oscillator stage (Q1, Q2) limits.

Q3 and Q4 provide a TTL compatible signal, which Q5 then converts to a sine wave.

00748308

Trace Vertical Horizontal

Top 5V/DIV

Middle 50V/DIV 500 µs/DIV

Bottom 0.2V/DIV

FIGURE 7. Various output levels are provided by the tuning fork oscillator shown in Figure 6.

This design easily produces a TTL compatible signal (top trace) because the oscillator is allowed

to limit. Low-pass filtering this square wave generates a sine wave (middle). The oscillator’s

0.7% distortion level is indicated (bottom) by an analyzer’s output.

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Resonant Element

Oscillator—Quartz Crystal

Quartz crystals allow high frequency stability in the face of

changing power supply and temperature parameters. Figure

8a shows a simple 100 kHz crystal oscillator. This Colpitts

class circuit uses a JFET for low loading of the crystal, aiding

stability. Regulation will eliminate the small effects (∼5 ppm

for 20% shift) that supply variation has on this circuit. Shunt-

ing the crystal with a small amount of capacitance allows

very fine trimming of frequency. Crystals typically drift less

than 1 ppm/˚C and temperature controlled ovens can be

used to eliminate this term (Figure 8b). The RC feedback

values will depend upon the thermal time constants of the

oven used. The values shown are typical. The temperature

of the oven should be set so that it coincides with the

crystal’s zero temperature coefficient or “turning point” tem-

perature which is manufacturer specified. An alternative to

temperature control uses a varactor diode placed across the

crystal. The varactor is biased by a temperature dependent

voltage from a circuit which could be very similar to Figure 8b

without the output transistor. As ambient temperature varies

the circuit changes the voltage across the varactor, which in

turn changes its capacitance. This shift in capacitance trims

the oscillator frequency.

Approximation Methods

All of the preceding circuits are inherent sine wave genera-

tors. Their normal mode of operation supports and maintains

a sinusoidal characteristic. Another class of oscillator is

made up of circuits which approximate the sine function

through a variety of techniques. This approach is usually

more complex but offers increased flexibility in controlling

amplitude and frequency of oscillation. The capability of this

type of circuit for a digitally controlled interface has markedly

increased the popularity of the approach.

00748309

(a)

00748310

(b)

00748311

(c)

FIGURE 8. Stable quartz-crystal oscillators can operate with a single active device (a). You can achieve

maximum frequency stability by mounting the oscillator in an oven and using a temperature-controlling

circuit (b). A varactor network (c) can also accomplish crystal fine tuning. Here, the varactor replaces the

oven and retunes the crystal by changing its load capacitances.

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Sine Approximation—Breakpoint

Shaper

Figure 9 diagrams a circuit which will “shape” a 20 Vp-p

wave input into a sine wave output. The amplifiers serve to

establish stable bias potentials for the diode shaping net-

work. The shaper operates by having individual diodes turn

on or off depending upon the amplitude of the input triangle.

This changes the gain of the output amplifier and gives the

circuit its characteristic non-linear, shaped output response.

The values of the resistors associated with the diodes deter-

mine the shaped waveform’s appearance. Individual diodes

in the DC bias circuitry provide first order temperature com-

pensation for the shaper diodes. Figure 10 shows the cir-

cuit’s performance. Trace A is the filtered output (note 1000

pF capacitor across the output amplifier). Trace B shows the

waveform with no filtering (1000 pF capacitor removed) and

trace C is the output of a distortion analyzer. In trace B the

breakpoint action is just detectable at the top and bottom of

the waveform, but all the breakpoints are clearly identifiable

in the distortion analyzer output of trace C. In this circuit, if

the amplitude or symmetry of the input triangle wave shifts,

the output waveform will degrade badly. Typically, a D/A

converter will be used to provide input drive. Distortion in this

circuit is less than 1.5% for a filtered output. If no filter is

used, this figure rises to about 2.7%.

00748312

All diodes = 1N4148

All op amps =

⁄

LF347

FIGURE 9. Breakpoint shaping networks employ diodes that conduct in direct proportion to an input triangle wave’s

amplitude. This action changes the output amplifier’s gain to produce the sine function.

00748313

Trace Vertical Horizontal

A 5V/DIV

B 5V/DIV 20 µs/DIV

C 0.5V/DIV

FIGURE 10. A clean sine wave results (trace A) when Figure 9 circuit’s output includes a 1000 pF capacitor.

When the capacitor isn’t used, the diode network’s breakpoint action becomes apparent (trace B).

The distortion analyzer’s output (trace C) clearly shows all the breakpoints.

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Sine Approximation—Logarithmic

Shaping

Figure 11 shows a complete sine wave oscillator which may

be tuned from 1 Hz to 10 kHz with a single variable resistor.

Amplitude stability is inside 0.02%/˚C and distortion is

0.35%. In addition, desired frequency shifts occur instanta-

neously because no control loop time constants are em-

ployed. The circuit works by placing an integrator inside the

positive feedback loop of a comparator. The LM311 drives

symmetrical, temperature-compensated clamp arrange-

ment. The output of the clamp biases the LF356 integrator.

The LF356 integrates this current into a linear ramp at its

output. This ramp is summed with the clamp output at the

LM311 input. When the ramp voltage nulls out the bound

voltage, the comparator changes state and the integrator

output reverses. The resultant, repetitive triangle waveform

is applied to the sine shaper configuration. The sine shaper

utilizes the non-linear, logarithmic relationship between V

and collector current in transistors to smooth the triangle

wave. The LM394 dual transistor is used to generate the

actual shaping while the 2N3810 provides current drive. The

LF351 allows adjustable, low impedance, output amplitude

control. Waveforms of operation are shown in Figure 14.

Sine Approximation—Voltage

Controlled Sine Oscillator

Figure 12 details a modified but extremely powerful version

of Figure 11. Here, the input voltage to the LF356 integrator

is furnished from a control voltage input instead of the zener

diode bridge. The control input is inverted by the LF351. The

two complementary voltages are each gated by the 2N4393

FET switches, which are controlled by the LM311 output.

The frequency of oscillation will now vary in direct proportion

to the control input. In addition, because the amplitude of this

circuit is controlled by limiting, rather than a servo loop,

response to a control step or ramp input is almost instanta-

neous. For a 0V–10V input the output will run over 1 Hz to 30

00748314

All diodes = 1N4148

Adjust symmetry and wave-

shape controls for minimum distortion

* LM311 Ground Pin (Pin 1) at −15V

FIGURE 11. Logarithmic shaping schemes produce a sine wave oscillator that you can

tune from 1 Hz to 10 kHz with a single control. Additionally, you can shift frequencies rapidly

because the circuit contains no control-loop time constants.

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Sine Approximation—Voltage

Controlled Sine Oscillator (Continued)

kHz with less than 0.4% distortion. In addition, linearity of

control voltage vs output frequency will be within 0.25%.

Figure 13 shows the response of this circuit (waveform B) to

a 10V ramp (waveform A).

00748315

Adjust distortion for

minimum at 1 Hz to 10 Hz

Adjust full-scale for 30 kHz

at 10V input

All diodes = 1N4148

* Match to 0.1%

FIGURE 12. A voltage-tunable oscillator results when Figure 11’s design is modified to include signal-level-

controlled feedback. Here, FETs switch the integrator’s input so that the resulting summing-junction current is a

function of the input control voltage. This scheme realizes a frequency range of 1 Hz to 30 kHz for a 0V to 10V input.

00748316

FIGURE 13. Rapid frequency sweeping is an inherent

feature of Figure 12’s voltage-controlled sine wave

oscillator. You can sweep this VCO from 1 Hz to 30 kHz

with a 10V input signal; the output settles quickly.

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Sine Approximation—Digital

Methods

Digital methods may be used to approximate sine wave

operation and offer the greatest flexibility at some increase in

complexity. Figure 15 shows a 10-bit IC D/A converter driven

from up/down counters to produce an amplitude-stable tri-

angle current into the LF357 FET amplifier. The LF357 is

used to drive a shaper circuit of the type shown in Figure 11.

The output amplitude of the sine wave is stable and the

frequency is solely dependent on the clock used to drive the

counters. If the clock is crystal controlled, the output sine

wave will reflect the high frequency stability of the crystal. In

this example, 10 binary bits are used to drive the DAC so the

output frequency will be 1/1024 of the clock frequency. If a

sine coded read-only-memory is placed between the counter

outputs and the DAC, the sine shaper may be eliminated and

the sine wave output taken directly from the LF357. This

constitutes an extremely powerful digital technique for gen-

erating sine waves. The amplitude may be voltage controlled

by driving the reference terminal of the DAC. The frequency

is again established by the clock speed used and both may

be varied at high rates of speed without introducing signifi-

cant lag or distortion. Distortion is low and is related to the

number of bits of resolution used. At the 8-bit level only 0.5%

distortion is seen (waveforms, Figure 16; graph, Figure 17)

and filtering will drop this below 0.1%. In the photo of Figure

16 the ROM directed steps are clearly visible in the sine

waveform and the DAC levels and glitching show up in the

distortion analyzer output. Filtering at the output amplifier

does an effective job of reducing distortion by taking out

these high frequency components.

00748317

Trace Vertical Horizontal

A 20V/DIV

B 20V/DIV 20 µs/DIV

C 10V/DIV

D 10V/DIV

E 0.5V/DIV

FIGURE 14. Logarithmic shapers can utilize a variety of circuit waveforms. The input to the

LF356 integrator (Figure 11) appears here as trace A. The LM311’s input (trace B) is the

summed result of the integrator’s triangle output (C) and the LM329’s clamped waveform.

After passing through the 2N3810/LM394 shaper stage, the resulting sine wave is amplified

by the LF351 (D). A distortion analyzer’s output (E) represents a 0.35% total harmonic distortion.

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Sine Approximation—Digital Methods (Continued)

00748318

MM74C00 = NAND

MM74C32 = OR

MM74C74 = D flip-flop

MM74193 = counters

FIGURE 15. Digital techniques produce triangular waveforms that methods employed in Figure 11 can then

easily convert to sine waves. This digital approach divides the input clock frequency by 1024 and uses the

resultant 10 bits to drive a DAC. The DAC’s triangular output — amplified by the LF357 — drives the log shaper

stage. You could also eliminate the log shaper and place a sine-coded ROM between the counters’ outputs

and the DAC, then recover the sine wave at point A.

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Sine Approximation—Digital Methods (Continued)

00748319

Trace Vertical Horizontal

Sine Wave 1V/DIV 200 µs/DIV

Analyzer 0.2V/DIV

FIGURE 16. An 8-bit sine coded ROM version of Figure 15’s circuit produces

a distortion level less than 0.5%. Filtering the sine output — shown here with a

distortion analyzer’s trace — can reduce the distortion to below 0.1%.

00748320

FIGURE 17. Distortion levels decrease with increasing

digital word length. Although additional filtering can

considerably improve the distortion levels (to 0.1% from

0.5% for the 8-bit case), you’re better off using a long digital word.

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Notes

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AN-263 Sine Wave Generation Techniques

National does not assume any responsibility for use of any circuitry described, no circuit patent licenses are implied and National reserves the right at any time without notice to change said circuitry and specifications.