The same can be said about the
height of the harmonics; although they
are calculated correctly and are accurate
relative to the fundamental, they also
look too low in absolute terms. So windowing
is no substitute for a coherent
When those objections were raised, I despaired that I was going to have to
return to the drawing board and maybe
stay there, or find a locked oscillator
with low distortion and noise or with
awesome postfiltering. How could I ever
make such a fundamentally analog oscillator
coherent to an FFT bin in such an
overwhelmingly digital environment?
At 5 kHz, a passive filter with notches
would be large and fussy. I thought of
detuning the Wien-bridge oscillator by
reducing the gain, thereby converting
it into a filter.
But then it occurred to me that a
gentle, analog sinusoidal nudge from
a distorting but well-locked external
oscillator might be enough to tweak
the Wien-bridge frequency to where it
needed to be. I decided to try injecting
a sinusoid into the input of the Wien-bridge
op-amp circuit, and opted to use
a high series impedance to avoid simultaneously
injecting noise and distortion.
I came up with 200k—about 1000× the
impedances already there—and put it
in as shown on the left side of Figure 4
(the “new input”). I set up the Agilent 33250A for a 5-kHz sine wave and
applied it to the new input. Looking at
both the 33250A and the Wien-bridge
outputs with an oscilloscope, I slowly
dialed up the 33250A frequency and was thrilled to finally see the sinusoids
come “close” and then snap into lock.
Figure 4 With the generators phase locked through the 10-MHz reference, the low-noise and -distortion Wien-bridge oscillator is gently nudged into coherence through the high-impedance, 200k resistor.
Click image to enlarge
I connected the 10-MHz back-panel
references and changed the 33250A
frequency to 5.157 kHz, the nearest
coherent bin in the FFT. The sinusoids remained in lock, and the programmable
33250A generator successfully
pulled the Wien-bridge oscillator
slightly away from its natural frequency
and into the desired frequency. The
result was a nearly ideal FFT; all of the
pertinent fundamental and distortion
powers were situated in unique bins and
were accurately represented (Figure 5).
Figure 5 A more accurate FFT is obtained using the same Wien-bridge oscillator but with the frequency injection locked to a coherent 5.157 kHz using an HP33250A driving the 200k resistor at the “new input.” Note that the peak is now visibly a believable –1 dBFS and that there is almost no power in the bins adjacent to the peak.
Programmable sinusoidal generators
often have excellent phase-noise
characteristics and 10-MHz locking
capabilities, but they also have high-output
wideband noise floors and distortion.
An FFT is sensitive to all of these
forms of source corruption and also has
a finite number of output bin frequencies.
To test high-performance analog
and mixed-signal systems, the right
combination of classical Wien-bridge
oscillators with programmable generators
can provide a nearly perfect source
with synchronous sampling, generating