Author Topic: Waveform Generating / Displaying Question  (Read 2460 times)

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Offline Electro Fan

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Waveform Generating / Displaying Question
« on: January 06, 2015, 04:22:56 pm »
Below are two images:

One from an Agilent DSO6014A displaying a sine wave generated by an older (but maybe pretty good) Krohn-Hite generator.

One from a Rigol DSO2072 displaying a sine wave generated with what I think are similar (frequency and amplitude) values generated by a somewhat newer BK Precision generator.

The sine wave on the Agilent appears to have smoother curves at the tops and the bottoms of the sine wave; the sine wave tops and bottoms on the Rigol appear somewhat sharper/pointier.  Are the slight differences in the curves likely due to differences in the way the scopes process and render the waveforms or the way the generators generate the waveforms?

Thanks, EF

- Added a photo of the sine wave generated from the BK Precision on a Tektronix 2247A analog scope - seems to have the pointy attribute
« Last Edit: January 06, 2015, 04:56:09 pm by Electro Fan »
 

Offline nfmax

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Re: Waveform Generating / Displaying Question
« Reply #1 on: January 06, 2015, 04:51:09 pm »
The 'pointy' sinewaves are a clear indication the waveform has been generated by a diode shaping network from an original triangle waveform. This is the classic technique used by analogue function generators since the '50s. Absence of such peaks is an indication either a true sinewave oscillator (e.g. a Wien bridge or L-C network circuit) or in this day & age a DDS has been used. It's nothing to do with the oscilloscope.

Do you have model numbers for either generator?
 

Offline Electro Fan

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Re: Waveform Generating / Displaying Question
« Reply #2 on: January 06, 2015, 05:03:14 pm »
The 'pointy' sinewaves are a clear indication the waveform has been generated by a diode shaping network from an original triangle waveform. This is the classic technique used by analogue function generators since the '50s. Absence of such peaks is an indication either a true sinewave oscillator (e.g. a Wien bridge or L-C network circuit) or in this day & age a DDS has been used. It's nothing to do with the oscilloscope.

Do you have model numbers for either generator?

Hi nfmax,

Thanks - I just posted an additional photo showing the sine wave from the BK Precision being displayed on a Tektronix analog (2247A) scope - it shows the pointy attribute; I think this confirms your thinking.  The BK Precision is model 4040A; I think the Krohn-Hite was a model 1600.

What are the trade-offs between the "50's" analog, Wien bridge, L-C network, and DDS techniques?  How about Agilent's Trueform?

EF
« Last Edit: January 06, 2015, 05:06:58 pm by Electro Fan »
 

Offline T3sl4co1l

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Re: Waveform Generating / Displaying Question
« Reply #3 on: January 06, 2015, 07:19:59 pm »
The BK just isn't made for low distortion, that's all.  Diode clipper circuits aren't inherently bad, they just have to be finely crafted to get good results.

Function generators (of the multivibrator / ramp / shaping vein) are excellent for fast and simple control, wide range, and other features like adjustable slew rate, PWM, triggering, gating (pulse trains) and so on.  The frequency is generally controlled with a simple proportional voltage, and can be adjusted through several decades in a single range.  The stability and drift are generally poor (dependent on precision voltages and resistors, thermal matching of internal amplifiers and converters, and non-ideal characteristics of the resistors, capacitors and comparators used to generate timing), as is the absolute speed (most go up to single digit MHz; personally, I have a somewhat faster Wavetek 193, which offers 20MHz capability; suffice it to say, its internal design is not straightforward!).

Wien bridge oscillators -- referring to not just the phase shift network (for which the twin-T network is also popular), but the traditional gain-controlled design as a whole -- offers reasonable adjustable range (usually up to a decade), very rarely electronic control (the adjustment is usually a gang-variable capacitor or resistor, not an electric current or voltage), and reasonably low distortion (sine wave) output.  The sine wave can be clipped to a square, but other waveforms (like triangle or PWM) are not available.  As with the proceeding case (they are both RC oscillators, at heart), stability, drift and ultimate frequency range are generally limited, dependent upon component properties, and rarely being used beyond a few MHz.

Like the Wien bridge oscillator, LC oscillators are generally used for sine waves, but at much higher frequencies.  Although inductors of large value can be constructed for very low frequencies (say, single Hz), they are very expensive and don't perform well.  As such, LC oscillators are confined to higher frequencies: most importantly, radio frequencies from perhaps 100kHz up.  As frequency is almost entirely dependent upon only two components, the inductor and the capacitor, they can be selected for high quality, and compensated against thermal drift, without getting terribly expensive in the process.  Adjustable range can be mechanical or electrical; in the old days, variable capacitors were preferred, occasionally using variable cores (variable reluctance or "slug tuned") to vary the inductor instead.  Electrical control is possible with saturable cores (a static magnetic field biases the core, reducing inductance) or varactor diodes (capacitance varies with voltage).  Frequency control is rarely linear, due to the inherent nonlinearity of these methods (cores do not saturate evenly; varactor capacitance varies inversely with voltage -- including due to signal voltage itself, causing distortion as well!).  Distortion can be made quite low, but it can also be poor, sometimes intentionally: old RF generators sometimes had an "extended" scale on the highest range, with an intentionally distorted output waveform, so that some power was still available at those harmonics.

LC oscillators are stable enough to remain within several Hz of a setting, making them fantastically useful for radio communications, where stable frequency references are required, such as for transmitting and receiving single sideband modulation (which is like AM, but with extraneous information removed, such as the carrier frequency; consequentially, even a fractional error in receiver frequency causes the voice to shift pitch, sound garbled or nasal, or completely unintelligible).

LC oscillators, in some form or another, extend well into the 10s of GHz range.  Above 500MHz or so, resonator type circuits become popular, as lumped inductors and capacitors stop being practical.  Though resonators are typically built using wideband transmission line structures, they can still be tuned in much the same way, though usually not over as wide a frequency range (a microstrip 1/4 wave stub might be tunable from 2-3GHz using a varactor, whereas a lumped oscillator might be capable of 50-100MHz or more -- a larger percentage, but a smaller difference range, too).  However, with a wider span comes a higher sensitivity to the same percentage-wise drift effects.  Whereas a 1MHz oscillator might have ppm drift of ~Hz, a 1GHz oscillator with even 0.01ppm drift (which would be astonishingly good even for a crystal oscillator!) still has ~10Hz drift.  Therefore, LC oscillators are often combined with a very stable quartz crystal oscillator, so that the crystal sets the majority of the desired frequency, while a lower frequency LC oscillator (which can be stable down to the Hz) sets a small adjustable change around the center frequency.

Bridging the gap between LC and DDS circuits, a PLL can be used to discipline an already fairly clean, but still somewhat drifty, LC oscillator against a very stable (but not adjustable) crystal oscillator.  As with the DDS, a modulo multiplication function is used to connect the signals ratiometrically.  The LC oscillator has to be voltage (or current) controlled over a useful range to implement this.  One perk of PLL techniques is, if the oscillator's control input is linear, then as the PLL varies that control input, it will exactly represent any variation in the signal being tracked.  If this is done on FM radio signals, the FM is demodulated implicitly by the receiver -- no need for an extra FM detector.

DDS techniques range from simply counting modulo N, to somewhat more advanced systems combining multiple stages together (cascaded DDSs to get better frequency control with cleaner outputs; PLL oscillators for sine waves, or lookup tables for arbitrary waveform generation; etc.).  Since the output is computed as a direct ratio to the system clock, the frequency can be very stable; but especially for frequencies very near unlucky multiples or fractions of the system clock, a variety of harmonic and anharmonic ("spurs") frequencies can be produced, in addition to the dominant (intended) signal.  Long term (slow) subharmonics and sidebands arise from counts which don't quite fill the counter register evenly.  Thus, after a run of, say, 100 cycles of output, maybe the 101st cycle happens to be just one system clock period longer than the rest, or whatever.

What counts as "lucky" or "unlucky" depends on system design and... fundamental number theory.

For instance, a binary counter can only represent steps of 1 / (2^N), so if you want a frequency of 500.000kHz from a system clock of 10MHz, yes, you must divide frequency by 20, which is straightforward, but to do it using a traditional DDS method, you must represent 1/20 as a limited length binary fraction.  Unfortunately, its binary fraction goes on forever, just as like 1/3 = 0.333... goes on forever in decimal.  Which means your output frequency won't be 500.000kHz, but rather, 500.001907...kHz.  Or if you build the DDS to accommodate that error, it will dither back and forth between 500.0019Hz and 499.9924Hz -- ultimately averaging the right frequency, but never quite getting it right.

And that's just for a square wave containing the timing but no "shape".  To generate an arbitrary waveform, the DDS register is piped through a conversion table, generating binary data, which is sent to a DAC.  If the table contains, say, all the values of sin(2*pi*x) for x = 0..1 (or whatever numerical range the DDS register is considered to represent), then the output will be a sine wave.  But an aggressive count will increment quickly, and the "sine" will be very steppy.  As a sampled waveform, the Nyquist theorem assures us that we can still recover the intended sine wave from that (or any other signal with bandwidth strictly less than half the sample frequency): but an ideal [reconstruction] filter requires infinite time delay (or a time machine -- just build your LC lowpass filter with flux capacitors, eh?), and doesn't have very desirable time-domain properties, so it's not very practical.

And notice... if the count is advancing slowly... then the output frequency is also slow.  So, yeah, your waveform comes through cleanly, but you can be huffing and puffing away with a freaking 1GHz system clock, just to end up with a triangle wave no better than the 20MHz signal my Wavetek can produce!  It's easy to hide inside a single silicon chip, but there are still a few good reasons why it's not the best solution for all problems.

As for Agilent's Trueform, it still has to conform to theoretical minimums -- but I don't know what all they do, so it could be quite good, I don't know.  Spur reduction is the biggest challenge in DDS design, and there are more than a few ways to address that (besides just cranking the system clock higher and higher).

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
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Offline Yago

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Re: Waveform Generating / Displaying Question
« Reply #4 on: January 06, 2015, 07:30:00 pm »
Thanks Tim, great post! :)
 

Offline Electro Fan

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Re: Waveform Generating / Displaying Question
« Reply #5 on: January 07, 2015, 01:37:18 am »
Tim, thank you for the very informative reply.  I will be studying it for a while!  Thanks! EF
 


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