Q5Power System Instrumentation

(a) Working Principle of Function Generator

A function generator is a signal source instrument capable of producing multiple standard periodic waveform shapes (sine, square, and triangular waves being the most common) over a wide, continuously adjustable frequency range, constructed around a core oscillator circuit that generates a triangular waveform, from which the other waveform shapes are further derived.

Core oscillator (triangle/square wave generation): a constant-current source alternately charges and discharges a timing capacitor at a constant rate, producing a linearly rising or falling voltage ramp across the capacitor (since a constant current into a capacitor produces a linearly increasing voltage, V=I*t/C). This ramp voltage is fed to a comparator (typically a Schmitt-trigger-type bistable comparator with hysteresis), which switches its output state (and correspondingly reverses the direction of the constant-current source charging the capacitor, via a feedback connection back to the current-source stage) whenever the ramp voltage reaches one of two preset threshold levels — this feedback arrangement causes the capacitor voltage to repeatedly ramp up to the upper threshold, then reverse and ramp down to the lower threshold, and so on, producing a continuous, symmetric triangular waveform at the integrator output, while the comparator's own output simultaneously provides a square wave (switching between its two output states at exactly the same rate the triangular wave reverses direction).

Sine wave shaping: the triangular waveform is further converted into an approximate sine wave using a non-linear wave-shaping network, most commonly a diode-resistor breakpoint network, in which progressively more diodes begin conducting as the triangular wave's instantaneous voltage rises further from zero, each conducting diode introducing an additional shunt resistance path that progressively reduces the effective slope of the output waveform as amplitude increases — by carefully selecting the breakpoint voltages and resistor values, this network approximates the curved, decreasing-slope shape of a true sine wave near its peak, converting the straight-line-segmented triangular wave into a reasonably good sinusoidal approximation (with the fidelity of this synthesized sine wave being the main design and calibration challenge in function generator design, particularly at higher frequencies).

Frequency and amplitude control: the output frequency is controlled by adjusting the magnitude of the constant charging/discharging current and/or the timing capacitor value (larger current or smaller capacitance giving a faster ramp rate and hence higher frequency), typically via a combination of a coarse range-selection switch (selecting among several capacitor values) and a continuously-variable frequency control (adjusting the charging current), while a separate output amplitude control stage (typically an adjustable attenuator or output amplifier gain stage) allows the generator's output signal level to be independently set for the intended test/measurement application.

Sweep and Voltage-Controlled Oscillator (VCO) Variants

Beyond the basic fixed-frequency function generator described above, many practical instruments extend the same core relaxation-oscillator architecture into a voltage-controlled oscillator (VCO), in which the constant-current source's magnitude (and hence the output frequency) is itself controlled by an externally applied DC control voltage rather than only by a manual front-panel knob, allowing the output frequency to be programmed electronically by another circuit or by a computer-controlled digital-to-analog converter. This VCO capability is, in turn, the basis of the sweep function offered on most general-purpose function generators, in which an internal, slowly-varying ramp or logarithmic sweep voltage is automatically applied to the VCO's control input, causing the output frequency to be automatically and continuously varied (swept) from a starting frequency to a stopping frequency over a settable sweep time — sweep operation is particularly useful for tracing out the frequency response (gain and phase-versus-frequency characteristic) of an amplifier, filter, or other network under test, since a single sweep automatically covers the entire frequency range of interest without requiring the operator to manually step through and record readings at each individual frequency point. Many modern function generators additionally provide voltage-controlled amplitude and DC-offset control, and some offer an external VCO input allowing frequency modulation (FM) of the generated waveform by an externally applied modulating signal, further extending the instrument's usefulness for communication-circuit testing and general signal-generation applications beyond the basic fixed-frequency sine/square/triangle output described above.

(b) Instrumentation Amplifier with Op-Amp

An instrumentation amplifier is a specialized differential amplifier configuration, most commonly built using three individual operational amplifiers, specifically designed to amplify the small voltage difference between two input signals while providing extremely high input impedance at both inputs and very high common-mode rejection ratio (CMRR) — a combination of characteristics that a simple single op-amp differential amplifier configuration cannot achieve simultaneously to the same degree, making the three-op-amp instrumentation amplifier the standard choice for amplifying small differential signals from transducer bridges (such as the strain-gauge Wheatstone bridge discussed in the preceding answer) in the presence of common-mode noise or interference.

Circuit structure and operation: the first stage consists of two op-amps (A1 and A2), each connected in a non-inverting configuration, with their non-inverting inputs directly receiving the two input signals V1 and V2 (giving very high input impedance at both inputs, since a non-inverting op-amp input draws negligible current), and their inverting inputs cross-connected through a shared gain-setting resistor network (typically three resistors, with the central resistor, Rgain, connected between the two op-amps' inverting input nodes) — this arrangement produces an amplified differential output between A1 and A2's outputs, with the overall gain of this first stage set by the ratio of the feedback resistors to the shared gain resistor Rgain, allowing the overall amplifier's gain to be conveniently adjusted using this single resistor value without disturbing the amplifier's balance or common-mode rejection performance. The second stage consists of a third op-amp (A3), connected in the standard differential amplifier configuration, which takes the two (now amplified) outputs from A1 and A2 and produces a final single-ended output voltage proportional to their difference, while any common-mode signal present at both A1 and A2's outputs (having passed through the balanced first stage without differential amplification) is rejected by this final differential stage's inherent common-mode cancellation.

Significance for instrumentation applications: this three-op-amp instrumentation amplifier topology's combination of very high input impedance (minimizing loading effects on sensitive bridge-type transducer circuits), conveniently adjustable gain via a single resistor, and excellent common-mode rejection (rejecting unwanted noise or interference signals that appear equally on both inputs, such as power-line hum pickup) makes it the standard, widely-used building block for amplifying the small differential output signals from strain gauges, thermocouples, and other bridge-based or differential sensor arrangements throughout industrial and power system instrumentation applications, typically available today as a single, pre-packaged integrated-circuit instrumentation amplifier device incorporating all three op-amp stages and precision-matched internal resistors for optimal performance.

Practical Significance of CMRR

The common-mode rejection ratio (CMRR), defined as the ratio of the amplifier's differential-mode gain to its common-mode gain (usually expressed in decibels), is one of the most important practical performance specifications of an instrumentation amplifier, because in real field wiring, the small differential signal from a bridge-type transducer is almost always accompanied by a much larger common-mode voltage appearing identically on both input leads — arising from sources such as capacitively or inductively coupled power-line interference (50Hz hum pickup along long signal cable runs from a remote transducer to the amplifier), ground-potential differences between the transducer location and the amplifier/instrument location in a large industrial plant, or DC bias/offset voltages associated with the bridge excitation supply itself. A high CMRR (typically 100dB or more for a good instrumentation amplifier) ensures that this common-mode interference, even though it may be many times larger in amplitude than the genuine differential signal of interest, is rejected to a negligible residual level at the amplifier's output, so that the final output faithfully represents only the intended differential signal from the transducer. Without adequately high CMRR, common-mode interference would be amplified along with the wanted signal (to whatever degree the amplifier's non-zero common-mode gain allows), corrupting the measurement with noise and potentially masking small genuine signal variations entirely — this is precisely why simple single op-amp differential amplifier circuits, whose CMRR is limited by the matching accuracy of their external resistors, are generally inadequate for bridge-transducer signal conditioning in industrial and power system instrumentation, and why the dedicated three-op-amp (or monolithic integrated) instrumentation amplifier topology, with its inherently much higher achievable CMRR, is the standard practical choice for this class of application.