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, Z_{x}, 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 v_{x} across the unknown impedance to be measured, Z_{x}. v_{x} is amplified and output as v_{vx}. The current through Z_{x} is i_{x} and is amplified by an inverting op-amp which creates a virtual ground at the bottom terminal of Z_{x}. Range-switched resistors R_{R} convert i_{x} to v_{ix} = i_{x}•R_{R}.

Voltage v_{g} of the sine-wave generator -- usually a Wien-bridge oscillator -- has an amplitude that is varied to control either v_{x} (for measuring C_{x}) or i_{x} (for L_{x}), using the source resistance of R_{g} (also switched) to control the range of oscillator current through Z_{x}. To measure inductance, v_{ix} is fed back to an oscillator amplitude controller that servos the peak v_{g} (variable v_{g} with the hat or caret over the v in Figure 1) to result in a given i_{x}. With i_{x} controlled to be V_{R}/R_{R}, then by measuring v_{x} and knowing the oscillator frequency ω_{g}, L_{x} 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 L_{x} or C_{x}. From the basic reactance equations,

This scheme is particularly effective in non-microcomputer-based instruments because if ω_{g} is adjusted accurately and i_{x} controlled, then together they provide scaling for the value of L_{x} as input to the V_{REF} input of a DVM IC while v_{vx} is input to the DVM measurement input as V_{x}. Then for L_{x} the display reads

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

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

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 R_{g} is redundant and is only used for control of current ranging because the resistors R_{R} have no control over bridge current. They only scale v_{ix}. When the DPDT switch of the switched-bridge scheme is in the L position, the op-amp virtual ground at the bottom of R_{g} sets the current through Z_{x} as i_{x} = v_{g}/R_{g}. Then –v_{x} 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 R_{g} is determined by the current-source input voltage, –v_{g}. This determines inductor current. For the C position, the voltage across C is held constant as –v_{g}. 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, v_{g}, 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 v_{g} is constant and i_{x} and v_{x} both vary with Z_{x} and R_{g}. The current amplifier uses R_{g} as a sense resistor, not unlike its use in the switched-bridge scheme, but without a virtual ground or the redundancy of R_{R}.

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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