# Z Meter on a Chip? Impedance Meter Range Capabilities

In the previous article in this series, we looked at bridge circuits used to measure impedance. Now, let's look at some more (simple) math.

Z-meter performance capability is expressed mainly by measurable impedance and frequency ranges. The Z-meter voltage and current of the unknown impedance, Zx , have measurement ranges that determine the overall resistance (R), inductance (L), and capacitance (C) ranges of the meter. The relationship is rather simple. If the voltage, vx , across Zx is measured over V decades and the current through it, ix , is measured over I decades, then the measurement range of Zx is Z = V + I decades, where Z, V, and I are ranges corresponding to the indicated variables and are on a log10 scale of decades. Therefore, the impedance measurement range of the meter extends from the minimum impedance magnitude of to a maximum impedance magnitude of The range of frequencies over which impedance is measured extends the measurement capability, as shown on the following reactance plot for Z meters. The frequency range, F, extends the reactance measurement range to

L = C = X = Z + F

The scaled bridge voltage and current, vvx and vix (discussed in my previous article), are converted to digital form and displayed by a digital voltmeter (DVM). DVMs have the quasistatic (low-frequency) transfer function of where VO is a digital displayed quantity with full-scale value of 2n counts, VX is the converted input voltage, and VREF , the reference voltage, is the full-scale value of VX . A ratiometric DVM converts the analog voltage ratio to a digital count ratio, and the division in the ratioing divides vvx by vix to give XX or RX when vvx and vix are correctly scaled.

The voltmeter range, including that of the DVM and its display, is an additional consideration. A DVM with more digits has more range, of course, though over that range, resolution (measured in counts) and accuracy decrease proportionally from the full-scale (FS) value. A meter with four digits has effectively one more decade of range than one with three digits for the same resolution. For the above range equations, the resulting values are relative to FS, whatever that might be for the DVM. The DVM itself can add additional range, depending on how the instrument accuracy is specified.

As an example, a B&K 875A handheld, battery-operated RLC meter has no range switching of AVX for its voltage measurement; V = 0 decades. The current amplifier range resistors, RR (from the previous article), span six decades from 10Ω to 1MΩ. Consequently,

Z = V + I; Z = 0 + 6; Z = 6 decades

This defines the range on the vertical (log ‖Z‖) axis of the above reactance plot. It corresponds to the full-scale resistance range of the meter: RX ϵ [20Ω, 20MΩ]. This meter has two excitation frequencies — 120Hz and 1kHz — giving it nearly 1 decade of F. Then

X = Z + F ≈ 6 + 1 ≈ 7

The B&K 875A does not make use of the highest L range (2kH); thus L = 6 decades FS (200μH to 200H). The lower frequency is included to extend the high end of the C range, and it is seven decades: 200pF to 2mF. The DVM is a 3.3-decade (3.5-digit) or 2,000-count meter. This results in a measurement range (with decreasing accuracy below FS) of 6 + 3.3 = 9.3 decades of total range for L and 7 + 3.3 = 10.3 for C.

In the next blog, we'll take a close look at the frequency sources used for excitation voltage of the impedance being measured.

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## 5 comments on “Z Meter on a Chip? Impedance Meter Range Capabilities”

1. Steve Taranovich
September 29, 2013

Thanks Dennis for the great tutorial and in-depth mathematical analysis.

I just wanted to comment on a neat use of a Z-Meter: Characterizing a thermoelectric element over a large temperature—The Z-meter can heat the sample to a very high temperature in a vacuum. The Z-meter can then simultaneously measure all three thermoelectric parameters (Seebeck coefficient, thermal conductivity, and electrical conductivity), as well as measure the generated power and the efficiency for a single TE leg.

2. September 30, 2013

@Steve – I would not have thought that the excitation voltage source on most Z-meters would have sufficient current drive capability to heat up much of anything – but perhaps some do….

3. Steve Taranovich
September 30, 2013

For very high temperatures, the power elements would probably have to be off on a heatsink to drive hefty current—although, class D drivers can run relatively cool and efficient

4. D Feucht
September 30, 2013

5. 