# Z Meter on a Chip? Impedance Meter Bridge Circuits

My wish list for highly-integrated measurement instruments includes impedance or RLC meters. These instruments are especially interesting because they allow for so many different design alternatives of their subsystems — all of which provides freedom in overcoming integration obstacles. I have chosen the impedance or Z meter for a detailed multi-article case study of what is involved for its monolithic integration. Before discussing integration strategies for Z meters, we start with the most exciting part, the core circuits themselves and some aspects of their design. From a familiarity with them, the integration consequences follow.

The core of a sine-driven Z meter is the bridge circuit. This is the circuit that includes the unknown impedance to be measured and which subjects it to voltage and current conditions from which its impedance can be determined. Shown below is a traditional engineering notebook page of two bridge-circuit schemes.

Figure 1 Upper op-amp circuit is the “classic” version. Lower op-amp circuit is the Innovatia version.

Not included are the first-generation schemes of manual bridges that depend on accurate (reference) capacitors and inductors to be built into the bridge. Reference reactances are not needed because a glance at a reactance chart shows that if we can measure both voltage and current through the unknown impedance, Zx , and know the frequency of sine-wave excitation, then we can calculate reactance from these values.

The bridge at the top of the drawing — the “classic” bridge circuit – as used in the HP4261A, ESI 253, and B&K 875A, has a voltage amplifier for measuring vx across the unknown impedance to be measured, Zx . vx is amplified and output as vvx . The current through Zx is ix and is amplified by an inverting op-amp which creates a virtual ground at the bottom terminal of Zx . Range-switched resistors RR convert ix to vix = ix &#x2022RR .

Voltage vg of the sine-wave generator — usually a Wien-bridge oscillator — has an amplitude that is varied to control either vx (for measuring Cx ) or ix (for Lx ), using the source resistance of Rg (also switched) to control the range of oscillator current through Zx . To measure inductance, vix is fed back to an oscillator amplitude controller that servos the peak vg (variable vg with the hat or caret over the v in Figure 1) to result in a given ix . With ix controlled to be VR /RR , then by measuring vx and knowing the oscillator frequency ωg , Lx can be calculated.

Another notebook page (recycling last year's calendar) is shown below. The circuit is drawn with more detail and the rest of the page presents the bridge equations and their derivations.

Figure 2 A bit more detail plus the equations.

The goal is to measure either Lx or Cx . From the basic reactance equations,

This scheme is particularly effective in non-microcomputer-based instruments because if ωg is adjusted accurately and ix controlled, then together they provide scaling for the value of Lx as input to the VREF input of a DVM IC while vvx is input to the DVM measurement input as Vx . Then for Lx the display reads

In other words, the division in Lx (and also Cx ) is performed by the ratiometric DVM. To measure Lx , the classic bridge keeps the current through Lx constant and known; to measure Cx , it keeps the voltage across Cx x constant and known.

Skipping down to the bottom bridge (shown below), the HP4271A gets rid of the need for a ranged Rg (less switching!) and in effect turns RR into Rg .

Figure 3 Upper circuit is the “Elektor” version. Lower circuit is the HP4271A version.

This “switched-bridge” scheme is an improvement over the classic scheme where Rg is redundant and is only used for control of current ranging because the resistors RR have no control over bridge current. They only scale vix . When the DPDT switch of the switched-bridge scheme is in the L position, the op-amp virtual ground at the bottom of Rg sets the current through Zx as ix = vg /Rg . Then –vx is the op-amp output voltage. It is a clean, simple scheme and can be used without a microcomputer to do the division. A DVM can do it.

The top circuit above is also a switched-bridge scheme. Designated as “Elektor” (from an article in the March, 1992 Elektor magazine by H. Kuehne), the bridge is a current-source variation on the bottom scheme. For the L position of the switch, the voltage across Rg is determined by the current-source input voltage, –vg . This determines inductor current. For the C position, the voltage across C is held constant as –vg . The whole bridge is within the op-amp current source circuit. The bridge equations, with slight notational adjustment, apply to all three schemes.

The HP4271A and Elektor schemes, having a switched bridge, have a slight disadvantage over the classic bridge schemes: They depend on the oscillator voltage, vg , in calculation of measured reactance. They also require the DPDT switch, which is a relay in a cold-switched instrument and can be integrated as CMOS switches. Oscillator amplitude control loops are needed in all schemes.

The Innovatia scheme is minimalist and Z-analyzer-oriented. The vg is constant and ix and vx both vary with Zx and Rg . The current amplifier uses Rg as a sense resistor, not unlike its use in the switched-bridge scheme, but without a virtual ground or the redundancy of RR .

In future articles of this series we will look at other blocks of the Z-meter functional diagram and their circuit implementation options. Meanwhile, a look at Z-meter ranging gives us a clearer overview of Z meters in a design context.

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## 12 comments on “Z Meter on a Chip? Impedance Meter Bridge Circuits”

1. samicksha
August 22, 2013

Interesting Blog although couple of things are new to me here, cuorious to understand about measurement of AC resistance and Z parameters.

2. D Feucht
August 23, 2013

Z or impedance meters do not measure z parameters as such. They measure resistance, inductance, and capacitance values. They also do not measure “ac resistance” caused by the skin and proximity effects within conductors as such, though if those effects manifest themselves at the excitation frequency of the Z meter, they will be included in resistance measurements.

3. CrunchFrog
August 25, 2013

You might want to take a look at Analog Devices' impedance meter on a chip, AD5933. It has an on chip oscillator, DDS, ADC and does DFT on board.  Control as well as Real and imaginary value recovery is via an I2C interface. Digilent are coming out with a Pmod to plug into various Dev boards.  (I am not affiliated with AD or Digilent).

August 26, 2013

@CrunchFrog – we'll take a look at the AD part and see what it can do and how well it can do it.

5. D Feucht
August 27, 2013

The AD5933 and AD5934 are what I would consider the core of low-frequency, digitally-oriented impedance analyzers. These are more than Z meters and would be the logical extension of the Z-meter-on-a-chip idea – though ADI has gone directly to the Z analyzer instead. These ICs are a great idea, in the same direction as the Z-meter IC.

That said, I still think there is a place for the Z meter because range switching and other aspects of a full instrument could be integrated on the Z-meter IC. There is a large enough market for Z meters (apart from Z analyzers) to merit such a develop, I surmise.

6. Steve Taranovich
August 31, 2013

Samicksha—Just break down the AC impedance measurement to simple circuits–an AC voltmeter and an AC ammeter to measuer AC impedances. Design those simpler devices and you have an AC impedance meter—check out sites like Keithley Instruments for more details.

As for Z parameters–look at this link http://www.egr.unlv.edu/~eebag/Chapter19.pdf

7. Navelpluis
September 18, 2013

Dennis,

In my little 'collection' of measurement equipment I have a HP4194 with a piece of servicedoc in digital form. The basic circuitry indeed is of alter importance: All performance will be depended of this. Very interesting stuff, very learning.

Everybody here with an analog background will love this piece of gear: Tonns of analog inside the HP4194 impedance analyzer. The basic principle resembles a lot of what Dennis wants to integrate in his chip, but then, approx 45x50x44cm piece of gear and it weighs a ton! 😉

(Section 8 in the HP4194 service doc explains the principles how this beauty works)

September 26, 2013

@Navelpluis – Is there a site we can go to and see that documentation? Do you have your own site on which you could post the documentation? It would be nice to see the schematics.

9. Navelpluis
September 26, 2013
September 26, 2013

@Navelpluis – I just looked at the manual. That's a nice piece of test equipment that I would like to own. Thanks.

11. richardlim
June 2, 2016

Can someone shed some light on how you calculate ESR after taking impedance measurements?  I must be missing something because for the life of me, I have been scratching my head on how to do that for the past 4 hours!

Thanks,

Richard

12. TimothyD921
June 8, 2016

Richard what does the circuit look like that you are taking measurements of?
If its an LCR circuit the ESR occurs at resonance. At resonance the two terms of reacatance cancel so all thats left is the ESR.

Timothy

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