# Z Meter on a Chip? Impedance Meter Oscillators

Impedance meter integration has multiple design options for the various functional blocks in a sine-driven Z meter. In this third article in this series, some of the circuit alternatives are considered for the major Z-meter functional blocks.

The first function block of Z meters is the sine-wave oscillator. The optimal analog choice (those that dominate Z meter products) is the Wien-bridge oscillator. Shown below is a fragment of a reverse-engineered circuit diagram for a B&K 875A that includes the oscillator and its amplitude stabilization loop (Figure 1) and (most of) the bridge circuit itself (Figure 2). (To its credit, B&K did provide me a circuit diagram, but it was borderline readable. Some tracing ensued.)

Figure 1

A portion of the B&K 875A schematic.

Figure 2

The Wien-bridge oscillator.

The typical Wien-bridge oscillator is implemented as shown along with circuit derivation. This oscillator is attractive for design because only Ri needs to be varied to vary the amplitude, and it is grounded.

Referring back to Figure 1, the two frequencies of the B&K 875A meter are switched by 2/3 of U1, a 4053 CMOS analog switch. As a DPDT switch, it selects both the feedback and input resistances for the op-amp to change frequency. The amplitude is stabilized by adjusting the gain of the inverting feedback loop with JFET Q2. Its channel resistance varies with gate voltage, from op-amp U4B. The U4B input is the error quantity of the amplitude stabilizer, the input of 1.5 V from the 220kΩ divider is matched by the fed-back peak sine voltage, extracted by the U3B half-wave peak detector. Whenever the U3B input is positive, the feedback diode, D1, conducts, charging C5 to the peak voltage. U3A is a switched-gain voltage amplifier that feeds back bridge voltage vvx or vix . U3A gain selection sets VR , the sine-wave output amplitude, to two possible values.

A nifty variation on loop stabilization is used in the Elektor Z meter design of H. Kuehne. It uses no JFET. The block diagram for the amplitude stabilizer is shown in Figure 3:

Figure 3

The design goal is to synthesize, at the oscillator frequency, the required Ri using a multiplier with feedback. The LM13700 is used as a variable-G ZM amplifier with output resistance of

Zi ≈ 1/(GM •IY •H)

where H is the voltage feedback attenuation. A simplified circuit diagram of half of the LM13700 is shown in Figure 4. This hidden treasure in the parts catalog has a BJT diff-pair input with matching base diodes and controllable emitter current-source BJT. The diff-pair output is made single-ended with current mirrors. Diodes Q11 and Q12 are unused. The LM13700 input voltage is the Zi -loop error voltage, which is near zero, and approximate multiplication is accurate enough. It is multiplied by IY which controls Zi .

Figure 4

A simplified schematic of half of an LM13700.

The complete amplitude control loop with oscillator is shown below in Figure 5 with a more detailed derivation of component values. The upper-right op-amp is the oscillator.

Figure 5

The oscillator sine-wave amplitude is extracted using a synchronous integrating peak detector. (Its derivations are in the boxed section to the right on the above notebook page.) During the positive half cycle, the zero-crossing comparator (LM13700 section B) turns on a switch that inputs the sine-wave to the integrator, along with a constant offset current, Io . The result is that the average sine-wave current into the integrator must equal the offset current out of it. The integrator output voltage is controlled by the loop to be some value of VY that sets IY and hence the transconductance gain, GM , of the LM13700 (section A).

Besides Wien-bridge oscillators, another type is the quadrature oscillators. The typical Z-meter implementation is shown in Figure 6:

Figure 6

It requires two op-amps but has the advantage of also generating a quadrature sine-wave (offset by 90° from the output of the first op-amp). Analog phase detectors need 0° and 90° waveforms to extract the resistive component of Zx and the quadrature oscillator provides it. Note however that changing the frequency requires varying three resistors.

The final category of sine-wave generators is digital, either by dedicated register logic (direct digital synthesis, DDS) or by microcontroller (μC) programming. DDS is used in waveform generators and is a more accurate and stable method for generation, though an analog phase-locked loop can also provide high frequency accuracy. A μC writing at regular intervals to two DACs can also output both sine and cosine waveforms for bridge excitation and as phase detector inputs.

All circuitry comprising the above oscillators and their amplitude control loops can be integrated, even the adjustment pots as digipots, if necessary. With μC calibration methods, however, few of these otherwise many adjustments found in Z meters are necessary.

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## 18 comments on “Z Meter on a Chip? Impedance Meter Oscillators”

1. David Maciel Silva
September 30, 2013

Great article Dennis,

In oscillators Wien lamp ever used to control the amplitude of the signal :)! At the time it was what could be done.

The advancement of uC and other devices made things easier, but the knowledge base remains the same, no concept of how a circuit of these works will be very complicated to put into practice on a uC.

Has anyone had to do a project using oscillators using a uC?

September 30, 2013

@Maciel – there is a circuit that used a very small incandescent lamp to control the feedback factor around the op-amp. Refer to Figure 2 in Dennis' blog. For the resistor labeled Ri, if you use a low value resistor (probably 10 ohms or lower) in series with a small lamp such as a #327 lamp; and the use Rf of 10 to 100 ohms; and then power the op-amp from +15 & -15V, you'll get a stable oscillator. The tungsten filament has a positive tempco, so the hotter it gets, the higher its resistance. Just right for this application.

3. D Feucht
September 30, 2013

@Maciel –

Lamp filaments as amplitude stabilizers were popular long ago but are not found much any more. They are highly nonlinear and this nonlinearity causes sine distortion. However, every amplitude stabilization scheme inherently introduces some nonlinearity. The multiplier in the Elektor scheme is a nonlinear element in the oscillator feedback loop.

Second, even small grain lamps are somewhat large relative to surface-mount components. They also change their resistance over time and this makes the amplitude subject to long-term drift. The multiplier or JFET overcomes much of these disadvantages.

4. Navelpluis
October 2, 2013

I reognize the JFET option: I once did a video AGC with it for a HAM television station. It had a double JFET in the feedback loop to avoid distortion. In this way it became extremely linear. The circuit was ment to 'level' the video to 1Vpp standard CVBS video level. Have a look at the Siliconix “FET Design Catalog” book, you may find it on the web, but fortunately I am a lucky bastard to have a copy at hand 😉

5. Man21
October 4, 2013

For a more dertailed analysis of the Wien bridge see 'Wave generation and shaping' by Leonard Strauss (McGraw Hill 1970, 2nd Edn. ISBN 0070-857-504 I think as the book only gives a Library of Congress #74-9002462161). See chapter 16 and particularly 16.2 and 16.5 relating to the effects of bridge balance on amplitude and frequency stability. See also ISBN 978-0-521-68780-5, section 5.8. See also Linear Technology AN43: Bridge Circuits, Marrying Gain and Balance, by Jim Williams, particularly pp29-33.

October 4, 2013

@Navelpluis – I remeber that data book – good source of material when I was tinkering with my own AGC circuits. Altho' mine were used for audio applications – audio compressors (my version of the Level Devil) for a home-brew recording studio; and guitar stomp-boxes. I think I still have my copy too.

October 4, 2013

@Dennis – quite right one all points. They were useful back in the day and for hobbyist projects tho'.

8. antedeluvian
October 4, 2013

For a more dertailed analysis of the Wien bridge see 'Wave generation and shaping' by Leonard Strauss

It was a proscribed book for us in 3rd year (1972), I think it was. I still have my copy as well.

9. Man21
October 5, 2013

I presume 'antedeluvian' meant prescribed rather than proscribed.

From even more antediluvian.

10. antedeluvian
October 5, 2013

Man21

I presume 'antedeluvian' meant prescribed rather than proscribed.

Given how badly I did at the subject, perhaps it was more proscribed than prescribed  for me.

11. kendallcp
October 7, 2013

I shall probably be shot down in flames and accused of heresy but… all these nice olf analogue oscillator circuits are lovely, but why not do it digitally with some form of synthesis technique.  I have been leaning towards filtering in the digital domain rather than the analogue domain for some while, and gerating sustained oscillation is another one of those things that can be done quite well digitally these days.  OK, I know it's not as much fun.  But it works well, and can be done with very low component count.

October 8, 2013

@kendall – well, it does feel a bit heretical, but I agre that some of the digiatl frequency synthesis methods are pretty slick: flexible and accurate. Hard to argue with that.

13. D Feucht
October 13, 2013

Hey Kendall,

As good engineers, we strive to be objective and suitably dispassionate in our analysis of the alternative solutions, and yes – DSP-based methods are quite in the running. (I just didn't want to give away any Really Good ideas in this series about them! – just the basics.) Hence the inclusion near the end of the article of “The final category of sine-wave generators is digital, …”.

There is a category of DSP techniques based on incremental function generation  that might be considered an outgrowth of the digital differential analyser (note correct spelling) work that went on, mainly in Britain after WW II. When implemented so that truly stable sinusoids are generated digitally, the result is quite attractive and would be one of the first methods to be considered in a Z meter IC implementation.

However, the analog schemes still have much going for them because they produce many bits of resolution for a few cheap analog parts which cost far less than a > 16 bit DAC. Happily, not too many bits of precision are needed for the Z meter oscillator unless one is pushing the state of the art in performance, and DSP generation is a front-line contender. So your point is well made.

14. davebirdieee
December 1, 2013

Dennis: Amplitude regulation of linear oscillators seems to be done exclusively through empirical methods. Do you know of any way to analyse the regulation path so as to be able to design similar to the usual feedback analysis? I've seen an article or two in the IEEE, but only as abstracts since I'm retired and not subscribed to their digital archive, and even then it's not completely clear that those articles address what I'm looking for.

Appreciate any insight you might be able to throw on this.

Thanks,

Dave

15. Victor Lorenzo
December 2, 2013

@D. Feucht, thanks for the article, I have to admit I still love seeing those hand drawed schematics ;).

However, the analog schemes still have much going for them because they produce many bits of resolution for a few cheap analog parts which cost far less than a > 16 bit DAC

One more thing to add is output filtering to remove the OOB noise introduced at converting signal from digital to analog domain (DAC), it will also add cost.

And even one more aspect to take into account is the DSP floating/fixed point precision, depending on the algorithm used for modelling the oscillator they could lead to instabilities that could lead to output saturation. Some generators simply use a bunch of memory to store one pre-generated pattern and then simply play it back.

16. D Feucht
December 2, 2013

Dave,
Not long ago, as part of my Z meter research, I spent a couple of weeks or more working on just this problem and have a detailed document on it. It could be submitted to Planet Analog for a short series on Oscillator Amplitude Control (which I probably will do), though if you are keen to see it, I can send you a MS Word copy if I receive your email address. It is about 341 kbytes in length and requires that the Word equation editor be installed.

What makes this a difficult control problem is that the loop is inherently nonlinear because multiplication in some form is present within the loop. My analysis is based on a JFET gain control mechanism, though the loop dynamics section is more general. Detection of the amplitude is not a trivial problem either.

The analysis assumes that the reader has a good familiarity with classical continuous control theory and with some DSP. (Hint: sinx/x shows up in the analysis of the peak detector.) Nonlinearity is handled by linear approximation around an amplitude loop operating point.

James Roberge, in his classic book, Operational Amplifiers, presents a method for analysis, but I think mine is more refined (nearly 40 years later!) and makes explicit some of the subtler assumptions in his scheme, though it is a good place to start.

I also do not have access to IEEE documents and will not pay the rather large amount an individual would have to shell out to have it. Perhaps the IEEE is intending to encourage originality and creativity, with perhaps some redundancy too, in making access to its papers unobtainable for so many.

17. D Feucht
December 2, 2013

Victor,

First, thanks for the encouragement in regard to hand-drawn circuit diagrams. They are sloppier than those from CAD editors or in published literature, but they also convey a sense of engineering as an art, which for the better engineers, it certainly is.

Your several points regarding the benefit of analog vs DSP are well-taken. One of the challenges of good design is knowing which combinations of analog and digital implementation will result in an optimum design.

18. davebirdieee
December 2, 2013

Dennis:

Thanks for the reply. I agree with all of your points. I've encountered them and agree. Yes, I'd like to see your paper. I have toyed with possibly using z transforms to do some of this, but haven't spent any time really looking at it.

Is there some special way to communicate my email or is it available through this board?

Agree with your comments re IEEE docs. Such a pity, and a loss. But, someone does have to pay.

Thanks again,

Dave

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