Design Article
Injection-lock a Wien-bridge oscillator
Glen Brisebois
10/31/2012 4:29 PM EDT
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I recently had the opportunity to investigate a new micropower 6-MHz LTC6255 op amp driving a 12-bit, 250k sample/sec LTC2361 ADC. I wanted to acquire the FFT of a pure sinusoid of about 5 kHz. The problem is that getting the FFT of a pure sinusoid requires, well, a pure sinusoid. Most programmable signal generators, however, have fairly poor noise and distortion performance, not to mention digital “hash” floors, compared with dedicated op amps and good ADCs. You can’t measure 90-dB distortion and noise using sources that are “60 dB-ish.” So rather than try to find and keep an almost-ideal programmable signal generator, I decided to build up a low-distortion Meacham-bulb-stabilized Wien-bridge oscillator using an ultralow-distortion LT1468-2 op amp (Figure 1).
 Figure 1 This Meacham-lightbulb-stabilized, low-distortion, low-noise 5-kHz Wien-bridge sinusoidal oscillator’s RC feedback network attenuates by a factor of 3 at its midband. The bulb’s self-heating forces a gain of 3 in the op amp. |
The lightbulb amplitude-stabilization technique relies on the positive temperature coefficient of the bulb impedance stabilizing the gain of the op amp to match the attenuation factor of 3 in the Wien bridge at its center frequency. As the output amplitude increases, the bulb filament heats up, increasing the impedance and reducing the gain and, therefore, the amplitude. I did not have immediate access to the usually called-for 327 lamp, so I decided to try a fairly low-power, high-voltage bulb, like the C7 Christmas bulb shown. At room temperature, it measured 316Ω; fresh out of the freezer (about −15°C), it measured 270Ω. Based on the 5W, 120V spec, it should be about 2.8k at white hot. That seemed like plenty of impedance range to stabilize a gain of 3, so I decided to linearize it a bit with a series 100Ω resistor.
For a gain of 3, the bulb plus 100Ω must be half of the 1.24k feedback (or equal to 612Ω), so the bulb must settle at 512Ω. Roughly calculating a resistance temperature coefficient of (316–270Ω)/[25−(−15°C)]=1.15Ω/°C means that the bulb filament will be about 195°C.
The oscillator powered up fine, giving a nice sinusoidal 5.15-kHz output at several volts, and independent measurements showed the second- and third-harmonic distortion products to be lower than −120 dBc. I applied the oscillator to the LTC6255 op-amp input after blocking and adjusting the dc level and ac amplitude, using the caps and pots as shown in Figure 2. The ac amplitude was adjusted for −1 dBFS, and the dc level was adjusted to center the signal within the ADC range. But, of course, this oscillator was purely analog and had no “10-MHz reference input” on the back to allow it to be synchronized with the ADC clock. The result is substantial spectral leakage in the FFT, so that it looks more like a circus tent than a single spike. Applying a 92-dB Blackman-Harris window to the data to reduce FFT leakage produced a fine-looking FFT (Figure 3).
Figure 2 The Wien-bridge oscillator drives the op amp and ADC pair under test. The resulting FFT is clean after windowing, but not exceptional, as Figure 3 shows.
Click image to enlarge
Figure 3 This 4096-point FFT was achieved using an unlocked oscillator with a 92-dB Blackman-Harris window. Note that the peak does not look like –1 dBFS and that there is power in the bins around the peak.
Although this FFT is accurate in some ways, a closer inspection reveals some problems. For example, the input signal is −1 dBFS, but it certainly looks graphically lower than −1 dB down. The reason is that even an excellent windowing function leaves some of the fundamental power in the frequency bins adjacent to the main spike. The software includes these bins in its power calculations, and rightly so, but the fact is that the spike looks too low to make a good photograph.
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LostInSpace2010
10/31/2012 9:47 PM EDT
Nice writeup of a clever solution to a common problem.
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MARK.THOREN
11/1/2012 2:43 PM EDT
Very nice, Glen!
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Rich in Elkhart
11/1/2012 5:26 PM EDT
Good circuit, I had forgot all about doing that. Some years back the Crown/Techron IMA intermodulation distortion analyzer used an injection lock method similar to this for its 60hz Wien bridge oscillator, to prevent beat notes against mains hum in the amplifier being tested!
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Roy McCammon
11/1/2012 11:20 PM EDT
Phase locks touch on deep reality. Nature abhors a vacuum, but loves a phase lock. Among the things that humans have come up with that ought not to work but do, a Phase locked loop is in the top 1%. If fact, it wouldn't work, except that it wants to.
I've never seen a PLL that didn't work, at least partly.
Build two oscillators that share a little supply coupling and they will phase lock. People can phase lock to the beat of music. They can dance, march and clap in unison. Fire flies can phase lock their blinkers. Jovian moons can phase lock. Clocks hanging on the same wall can phase lock. The electric grid phase locks. Synchronous motors phase lock.
It occurs to me that if I add two sinusoids of amplitudes A and B (which I am not allowed to change), and frequencies f1 and f2 (which I can change) and phases p1 and p2 (also which I can change), that if f1 and f2 are different, then the power is A^2 + B^2, but if I set f1 = f2 then I can adjust the phase such that the power varies between A^2 + B^2 -2AB and A^2 + B^2 +2AB and thus I might make some argument about phase locking achieving some grand energy minimization or maximization.
Oh well, just speculating.
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Radcliffe
11/3/2012 3:06 PM EDT
Glen did everything right for injection locking. He only used a small signal for the lock, which is the right way to do it.
A sine wave is not necessary for a good injection lock. Pulses can be used; the signals lock on the rising edges.
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WKetel
11/5/2012 10:13 PM EST
Definitely an elegant solution to the problem. It also points out how sensitive an oscillator can be to external influences, both stabilizing and de-stabilizing. That is the other benefit of using phase locked loops, it is the phase stability.
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Bob C.
11/8/2012 10:29 AM EST
Nice detective work, and updating of an old workhorse.
The first commercial product of Hewlett-Packard was the 200A Wein-bridge oscillator (they appended the 'A' to make it look like a revision and that they had been in business longer than just being a startup). The oscillator design was Bill Hewlett's Master's thesis at Stanford. Disney Productions bought eight of these units to check out their audio equipment for the movie 'Fantasia'.
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JSOUSA_#1
11/13/2012 11:17 AM EST
Glenn, this is a great continuation of the Wien Bridge oscillator tradition. I had never seen a very linear Wien Bridge oscillator "locked" with a simple injection, and it was not until I saw your elegant design that I realized that the "lock" mechanism is very different from that of non-sinusoidal oscillators with non-linear circuits in the oscillation loop, like triangle or square wave oscillators. With the very high linearity of this oscillator (~90dB=0.003%), there is no easy mechanism to retard or speed up individual cycles by modulating the circuit non-linearity with the external injection. As I have come to understand it, the injected sine wave into your oscillator presents itself as additional signal to the AGC element, in the form of increased power to the light bulb, which then increases it's temperature and drops the net loop gain at the oscillation frequency below 1. This makes the natural oscillation disappear as it is replaced by an amplified and filtered version of the lock signal input. Reasonable results might be obtained even with injected square waves, if these are very close to the natural frequency and are thus extensively filtered by the very high working circuit Q. A Q=1000 would be a plausible operating Q at some locking frequency and amplitude. It would be good to find a paper explaining all this with rigor, as all kinds of interesting and useful relationships between lock distance and locking signal amplitude could be explored. For example, as the locking signal amplitude is increased or the locking distance increased, the loop gain drops further and the operating Q and bandwidth drop, resulting in shallower harmonic filtering. Perhaps HP's Bernard Oliver, who designed the HP200CD and the extraordinary HP207, wrote on locking linear sinewave oscillators. Summarizing, after "lock" the Wien bridge no longer oscillates at it's natural frequency and becomes a very high-Q filter operating under AGC (Automatic Gain Control).
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Glen Brisebois
11/13/2012 2:16 PM EST
Actually the oscillator itself was much better than 90dBc: more like 120dBc. But the circuit under test was on the order of -90dBc.
By the way, I wrote this when Jim Williams was still alive, and this particular Wien bridge using LT1468-2 was the last thing I talked with him about. We wondered why the distortion was so good even though the Vcm was moving, but that does seem to be a nice feature of the LT1468 family. Anyway, I put the oscillator in a loop to null the common mode and the distortion got worse, so I stopped pursuing that.
I don't think the lock has much to do with the AGC function or bulb power. Maybe that would have been the case if the 200k was much a lower impedance. Injecting to the bulb side is preferable from a pure science standpoint because it doesn't have an impact on the Wien bridge impedances. (Either side should work though, because opamp inputs are wonderul things.) Injecting weakly is preferable because the distortion and noise of the injector doesn't degrade the oscillator performance.
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