In the first two parts of this article, the first two generations of triangle-wave generator loops were presented – the foundational concepts at the heart of function generator (FG) technology. This article extends farther, into interesting extrapolations such as differential triangle-wave generators, including one that automatic controls waveform symmetry for low-distortion sine-waves. Another is a sweeping FG scheme that implicitly generates exponential sweeps for magnitude frequency plots. Sine shapers in earlier FGs were resistor-diode piecewise-linear circuits that have been supplanted by translinear function generation. Also, multiple function-enhancing circuits are added to FG instruments.

**Differential TWGs**

Another variation on the triangle-wave generator (TWG) is to make the generator loop differential, as shown below. This is a simplified circuit of the Exar 2206 FG IC.

In this circuit, the timing capacitor, *C* , is not grounded but is suspended differentially between current-source switches. To maintain an accurate waveform, the diff-amp following the loop must be able to reconstruct the two waveform fragments into a continuous (“glitch-free) waveform. A differential TWG was also used, with higher performance, in the HP3314A.

**Autosymmetric FG**

The fuller benefit of differential waveform generation was realized in the Tek FG506 prototype (never introduced as a product), shown schematized below. The difference in value of the two timing capacitors is corrected by sensing the sum of the differential waveforms and amplifying it as differential error. The –*I _{T} * current source is then driven by the error to keep the waveforms symmetrical.

This auto-symmetry scheme is able to maintain symmetry over four decades of frequency sweep, a feat that is essentially infeasible with previous schemes. Asymmetry is a major cause of sine distortion and a sine sweep over four decades was featured in the FG506.

The block diagram, shown below, of the FG506 illustrates what is involved in a sweeping FG with autosymmetry.

An additional flourish, shown below, is the generation of an exponential sweep frequency (by the “sweep gen” block) so that by sweeping an audio amplifier or other device under test with a four-decade sine-wave (10 Hz to 100 kHz), a Bode magnitude plot can be presented on an oscilloscope screen by observing the sine amplitude across the screen. Exponential sweep causes the horizontal ‘scope axis to be displayed as a logarithmic axis. Nowadays, with microcontrollers, this simple technique is still applicable because FG frequencies often exceed maximum μC interrupt rates.

The voltage-controlled frequency (VCF) input to the triangle-wave generator, *v _{F} * , is an integrated current pulse,

*I*of fixed duration

_{F}*τ*<

*T*, where

*T*= 1/

*f*. Hence a fixed charge is dumped into

*C*when the one-shot (MMV) is triggered each cycle of the TWG output. Consequently,

_{F}*v*increments by Δ

_{F}*v*each cycle;

_{F} The rate of change in *v _{F} * (

*t*) over an interval of Δ

*t*is

For many cycles, *n* , during the frequency sweep, the rate can be approximated by a derivative;

The TWG output frequency, *f* , depends on *v _{F} * by scale factor,

*K*, and

_{F}Then combining equations,

This first-order differential equation has the solution,

and frequency is thus swept exponentially:

In a μC-based FG, the same basic principle can be used to simplify software generation of the exponential by avoiding calculation of the exponential function. Instead it results from incremental function generation. At low FG frequencies, for each FG cycle the μC is interrupted and *v _{F} * is incremented by an amount that determines frequency sweep rate. FG frequencies can easily exceed what even a fast μC can process and the FG frequency is instead input into a μC counter by which frequency can be measured and

*v*controlled. During sweeping, the counter is set to overflow every

_{F}*N*cycles, causing an interrupt in which Δ

*v*is applied.

_{F}*N*depends on the low and high frequency limits of the sweep. For wideband sweeps, however, the analog circuit remains feasible and perhaps preferred, to keep what in the μC is

*N*= 1 so that the low frequencies are swept through in a shorter time. A low frequency of 1 Hz can result in a sweep lasting seconds.

**Additional FG Functions**

**Sine Shaper**

Besides the basic TWG loop which outputs triangle- and square-waves, a sine-wave is part of the FG repertoire of functions. As in the above FG circuits, a diode-resistor network was used early in FG history as a piecewise-linear function shaper. One of several clamping circuits per shaper is shown below.

Usually three or four of these circuits are paralleled and use a common output resistance, placed between the shunt *R _{o} * of the segments and ground. By adjusting breakpoints with

*R*and slopes with

*R*, total harmonic distortion (THD) can typically be reduced at audio frequencies to around 0.1 %.

_{o}By using translinear circuits, this can be reduced further and kept lower at higher frequencies. Translinear circuits are based on the matching of BJT *b-e* junctions and the ability to generate power-series functions using them. For instance, a three-term Taylor-series expansion of the sine function for two quadrants is implemented by the circuit shown below. The emitter-coupled BJT pair current sources are ratios from the coefficients of the sine series.

An improved and simplified four-quadrant sine generator is shown below. It is driven by a differential triangle-wave current and the output is a differential sine-wave. Art Metz developed it and Tektronix holds an expired patent on it.

THD values of well under 0.1 % can be achieved with this circuit.

**Control of Amplitude, Frequency, Symmetry, and Gating**

Because of the versatility of FG circuitry, it is possible to give the user control of several waveform parameters. In addition to the voltage-controlled frequency (VCF) input, a multiplier provides amplitude control for amplitude modulation of the waveforms. The two timing-current sources allow for independent control of each half of the cycle. Symmetry can be varied in some FGs by an input voltage, but in many, the waveform selection function provides some fixed symmetries – usually 10 % and 90 % values that result in ramps, reverse ramps, and pulses. Sines with asymmetric half-cycles are also a fallout of the FG circuits though they are seldom offered as user selections; they are of dubious utility as waveforms though they do occur in some digital phase modulation techniques.

What can be of use is the gating of waveforms by an external voltage input. The waveform is turned on and off. Of greater utility is the phased gating of FG waveforms. The Tek FG501 has a control whereby the starting phase can be adjusted. In another variation, *N* cycles can be synchronously gated and counted for *N* -cycle burst generation.

Presentation of the output can vary depending on the power amplifier that drives it. A 50 Ω output resistance is standard. Amplitude can range from 5 V for fast generators to +/- 20 V for versatile ones. Output offset control adds versatility. A FG differs from a PG in that amplitude and offset must be varied interactively for setting desired high and low pulse or peak and valley levels. However, there is no reason that *amplitude processing* in Fgs need be any different than in PGs.

I cover FG and related circuits in the *Analog Circuit Design* book series in volume 4, *Designing Waveform Processing Circuits* , SciTech Publishing which is also found on bookseller websites.

Dennis:

In this piece you say that the diff-amp following the timing capacitor

must be good at “reconstructing” the two triwave fragments shown in

the figure. That's one way of looking at it; but in fact the voltage that

appears across the capacitor is already a (near-) perfect triwave. I've

used schemes of this sort (though using a better core implemented as

a multi-decade linear voltage-to-frequency converter – like the AD537

or AD654) in sinewave synthesis with no “glitch” problems. Barrie

Hi Barrie,

I suspect that your ADI parts were implemented with a better differential triwave generator than that of the XR2206 as shown in the article. It had some fast edges on the waveforms on each side of the timing capacitor and this caused some glitching in the waveform, even at 1 MHz speeds. The diff-amp couldn't follow them precisely. HP FGs such as the 3314A did a better job and produce clean waveforms.

I continue to marvel that the work you did on both translinear function (sine in this case) generation

andmulti-tanh circuits is not being used widely. The patent on multi-tanh must be expired by now, yet the multi-tanh concept has yet to become common household engineering banter. It was a concept that is still ahead of our time.If you do not, maybe I'll do a future Planet Analog article on it. Few are probably aware of your multi-tanh IEEE paper(s), and an explanation of the

fundaments(note that I now – thanks to your comment long ago – use the noun form instead offundamentals; when willchiropracticbecomechiropraxis? Andschematicbecomescheme?) might stir some renewed interest in it.Sure Dennis, go ahead:

I am up to the gills in product design and have little time at the moment

to engage in the writing of tutorials. The M-tanh idea now has numerous

children and followers in many new ICs. It's not flawless – no circuit ever

is – but when implemented with sufficient care it proves to be very useful.

It is also implemented now in its less obient CMOS versions, using either

sub-threshold operation or strong inversion.

Your tutorials are always enjoyable and clearheaded. Thanks.

Best regards,

Barrie