**Experiments
with ADE-1 Mixer as Phase Detector**

**Sam
Wetterlin**

**12/6/06**

A 1MHz square wave
was amplified by a MMIC and used as the LO for a Mini-Circuits ADE-1
Mixer. A 1MHz sine wave synchronized
with the square wave was used as the RF.
The signal generator creating the sine and square waves could precisely
vary the phase of the sine wave relative to the square wave. The IF output was filtered with a low pass
filter to get a DC output whose level depends on the RF signal level and the
phase difference between the two signals, as described below.

The LO drive is a
bit uncertain, but I use 10dbm since that is approximately the saturation level
of the AD8354 MMIC used to amplify the LO.
The MMIC was overdriven by perhaps 3db beyond what should have been required
to produce 10dbm output.

The RF was varied
from -40dbm to -10dbm for various experiments.
Shown in Figure 1 is the output with a -33dbm RF level, for phases from
0 to 180 degrees. Zero degrees is a
somewhat arbitrary point which I adjusted to be close to zero output, but there
is a slight offset. There is also about
a 2.5mV offset in the ADE-1 dc output level, probably due to imperfect matching
of diodes or transformers.

**Figure 1**

Figure 1 shows
that the measured values can be very closely fit with a sine wave (which takes
into account the offsets mentioned above).
In fact, the fit almost everywhere is accurate to +/-0.1 mV, which is
the limit of my voltmeter.

Figure 2 shows a
similar graph with the RF level increased to -13dbm. At this level, the slopes become more linear
and the measured values can be better approximated with a triangle wave, at
least in areas not too near the peaks.

**Figure 2**

Based
on the apparent trend from Figure 1 to Figure 2, one might expect that the
triangle approximation would become very good at high RF levels. To test this out, I increased the RF level to
5dbm as shown in Figure 3.

**Figure 3**

Curiously,
the measured peaks at high RF levels become asymmetric, and the triangle
approximation is good only within about 60 degrees of zero. I obtained similar results with an RF level
of -3dbm. Perhaps somewhere between -13dbm
and -3dbm, the linear fit could be optimized, but the target RF range would
likely be pretty narrow.

If
the RF signal to be measured could be amplified to a fixed level with an AGC
amplifier, accurate phase measurements could be made by using an RF level of
-13dbm per Figure 2 and utilizing a quadratic approximation for the upslope and
downslopes. The curvature of those
slopes is gentle enough that a quadratic approximation should be very good. It
would also be necessary to avoid the areas near the peaks by an appropriate
phase shift.

For
a variable RF level, it would be best to keep the RF level below -25dbm and use
a sine wave approximation. Even in this it
is best to avoid the peaks because the output level between, say, 90 degrees
and 91 degrees is difficult to distinguish because of the flat slope.

It
is also possible to use the mixer to determine both magnitude and phase of the
RF signal, by taking two measurements, one with the RF shifted by 90 degrees
(or any known amount in the vicinity of 90 degrees). I won’t go into the math here, but I was
interested in how accurately the mixer output would correspond to theory. In theory, the dc output will equal
K*V*cos(θ), where K is a constant, V is the RF signal level, and θ is
the phase angle difference between the RF and LO signals.

We
can see from Figure 1 that the output is indeed proportional to the sine of the
phase angle as used in Figure 1. To
convert the sine to cosine, the arbitrary reference for zero phase just has to
be shifted 90 degrees. But we can also
see from Figure 2 that if the RF level is too high, the sine wave gets
distorted into a triangle wave. To avoid
that distortion, I believe the RF signal cannot exceed approximately -25dbm

I
also made measurements of the peak positive and negative output levels for
various RF levels from -43dbm to -13dbm to see if the peaks were proportional
to RF signal level. Those peak measurements
also provide the value of the dc offset level, which is:

**DC Offset= (Peak positive +
Peak negative)/2**

This is a
relatively simple measurement, because the peaks are so broad that you can move
by a few degrees with minimal impact on the DC output.

As an aside, I
found that the DC offset varied with the RF signal level if the LO level is not
strong enough. I also found that
different RF levels created different phase offsets when the LO level was
inadequate. When I settled on the 10dbm
level described above, the offsets stabilized at 2.4 mV and the phase offset
did not change when I changed the RF level.

The values I
obtained for peak positive/negative are as follows (values in mV):

__RF level____à____ -13dbm -23dbm -33dbm -43dbm__

Positive 207.8 155.9 53.2 18.5

Negative -203.1 -151.1 -48.3 -13.6

Offset 2.35 2.40 2.45 2.45

In theory, the
ratios of positive peaks (less DC offset) for RF levels 10db apart should be
the square root of 10, or 3.16. In fact,
they came out as follows (all DC values have had the DC offset subtracted):

DC_{-13dbm}/ DC_{-23dbm}^{
}= 1.34

DC_{-23dbm}/ DC_{-33dbm}^{
}= 3.02

DC_{-33dbm}/ DC_{-43dbm}^{
}= 3.16 ß Perfect!

For high RF
levels, the DC output clearly gets compressed, so the values at RF=-13dbm are
far lower than they should be. It
appears that RF=-23dbm is slightly beyond the maximum permissible level to
preserve a linear relationship between RF signal level and DC output. Levels below -43dbm would also be acceptable,
with the lower limit being the point where drift in the DC offset becomes a
significant part of the measured DC value.

**Conclusion**

To preserve the
relationship DC= K*V*cos(θ), the RF signal level cannot exceed
approximately -25dbm. However, to use
the mixer as a phase detector only (i.e. no determination of magnitude), a
fixed RF signal level near -13dbm will establish a reasonably close triangle
wave relationship between phase and output, which could be accurately
approximated with a quadratic fit to the upslopes and downslopes.