Injection Locking a Wien Bridge Oscillator

I recently had the opportunity to play around with a new micropower 6MHz LTC6255 op amp , driving a 12-bit, 250 kS/s LTC2361 ADC. I wanted to take an FFT of a pure sine wave at about 5kHz. The problem is, to get an FFT of a pure sine wave, you need a pure sine wave. But most programmable signal generators have poor noise and distortion performance, not to mention a “noisy” digital background compared to a dedicated op amp and a good ADC. You can’t use a “about 60dB” source to measure 90dB of distortion and noise. So instead of trying to find a near-ideal programmable signal generator, I decided to use an ultra-low distortion op amp, the LT1468-2, and make a low-distortion Meacham-bulb-stabilized Wien-bridge oscillator (Figure 1).

The amplitude stabilization technique for the bulb uses the positive temperature coefficient of the bulb's impedance to stabilize the op amp's gain to match the attenuation factor of 3 at the center frequency of the Wien bridge. As the output amplitude increases, the filament heats up, increasing the impedance, reducing the gain and thus the amplitude. I didn't have the usual so-called 327 bulb on hand immediately, so I decided to try a lower-power, high-voltage bulb, the C7 Christmas light in Figure 1. At room temperature, its impedance measured 316Ω, and after being chilled (about 15°C), it measured 270Ω. At 120V, 5W, it should be 2.8k in its white-hot state. There seems to be an impedance range where a gain of 3 can be obtained stably, so I decided to connect a 100Ω resistor in series with it to make it more linear.

At a gain of 3, the sum of the bulb and 100Ω must be half the 1.24 kΩ feedback (or 612Ω), so the bulb must settle at 512Ω. A rough calculation using the resistance temperature coefficient of (316-270)Ω/[25-(-15)] = 1.15Ω/ gives a filament temperature of about 195°C.

The oscillator started up fine, with a nice 5.15 kHz sine wave of several volts at the output, and separate measurements showed that its second and third harmonic components were both less than -120dBc. After blocking and adjusting the DC level with the capacitors and potentiometers in Figure 2, the oscillator was applied to the input of the LTC6255. The AC amplitude was adjusted at -1dBFS, and the DC level was adjusted to center the signal in the ADC range. However, this oscillator is purely analog, and there is no "10MHz reference input" in the background to synchronize with the ADC. The result is significant spectral leakage in the FFT, so it looks more like a circus tent than a pulse. To reduce the FFT leakage, a 92dB Blackman-Harris window is applied to the data, which gives a nice FFT (Figure 3).

Although this FFT has some accuracy, a closer inspection will reveal some problems. For example, the input signal is -1dBFS, but looking at the graph it is clearly below -1dB. The reason for this is that even a good windowing function will leave some fundamental power in the frequency window around the main pulse. The software includes these windows in its power calculations, as it should, but the fact is that the pulse is too low to make a good graph.

The same thing happens with the harmonic heights, although they are calculated correctly and are accurate relative to the fundamental, their absolute terms also appear too low. So, for a coherent phase-locked system, there is no substitute for windowing.

When I discovered these shortcomings, I desperately thought I would have to go back to the drawing board, or find a locked oscillator with low distortion and low noise, or have super good post filtering. How could I make a basic analog oscillator consistent with an FFT window in this advantageous digital environment? A notched passive filter at 5 kHz would be large and complicated. I planned to detune the Wien bridge oscillator by reducing the gain, thus converting it into a filter.

But it occurred to me that a simulated sine wave would be distorted, but a well-locked external oscillator might be enough to modify the Wien bridge frequency to the desired value. So I decided to try injecting a sine wave into the input of the Wien bridge op amp circuit, and chose a large series impedance to avoid injecting both noise and distortion. I wanted to use a 200 kΩ impedance, which is about 1000 times the existing impedance, and put it on the left side of Figure 4 (the "new input"). I set the Agilent 33250A to a 5kHz sine wave, applied it to the new input, and used an oscilloscope to observe the 33250A and the Wien bridge output at the same time, and then slowly turned up the 33250A frequency. I nervously watched as the two sine waves finally "coincidentalized" and entered a locked state.

I connected a 10MHz backplane reference signal and changed the 33250A's frequency to 5.157kHz, the closest coherent window in the FFT. The two sine waves remained locked, and the programmable 33250A generator successfully pulled the Wien bridge oscillator slightly off its natural frequency to the desired frequency. The result is an almost ideal FFT. All coherent fundamental and distortion powers are located in a single window and are accurately represented (Figure 5).

Programmable sine wave generators typically have very good phase noise characteristics, and 10 MHz lock capability, but they also have high output bandwidth background noise and distortion. An FFT will be sensitive to all of these forms of corruption sources, and also have a fixed number of output window frequencies. For testing high-performance analog and mixed-signal systems, the proper combination of a classic Wien bridge oscillator and a programmable generator can provide a near-perfect synchronous sampling signal source for accurate FFTs.