The following measurement system is designed to obtain the root mean square (RMS) voltage of sine waves without any dc component, such as .

The first stage operates as a full-wave rectifier with gain , as shown in the input-output characteristic in the figure below. The second stage consists of an averaging circuit with gain .

Assuming , determine such that the output voltage corresponds to the RMS value of the input signal .

Consider the following circuit designed to obtain the root mean square (RMS) voltage of sinewaves (without any dc component).

The first stage operates as a half-wave rectifier with the input-output characteristic depicted below. The second stage consists of a multi-feedback low-pass filter (LPF) with unitary inverting gain (i.e., in the passband) and a cutoff frequency () much lower than the frequency of the input voltage signal .

Assuming , determine such that the output voltage corresponds to the RMS value of the input signal .

In the figure below it is depicted the spectral components of two signals, and , corresponding to the inputs of the circuit shown.

Obtain assuming that the RMS value of the current is .

Consider a square-waveform signal with zero mean value, as shown in the figure, where its root-mean square (RMS) value is .

Consider that, in a second phase, a half-wave (ideal) rectification is performed with as input, obtaining the signal shown in the figure.

Finally, the continuous component (dc) of is removed, obtaining the signal .

Determine , i.e. the RMS value of .

Consider the measurement of the DC output voltage of a device under test (DUT), which consists of a voltage regulator, as shown in the figure. To obtain the voltage output for a given load , a 4  digital multimeter (DMM) was used as a voltmeter, always selecting the most adequate measurement range for the readings.

A large number of independent voltage readings were taken, with . This resulted in an average value and a standard deviation .

Determine the absolute value for the expanded combined uncertainty (from types A and B uncertainties) at a 95 % confidence interval.

The DMM manufacturer’s accuracy for the DC voltmeter is provided in the table below.

Consider a regulated voltage output that needs to be checked. Three colored DC digital bench voltmeters (DVM) are available: red (DVM-1), green (DVM-2), and blue (DVM-3). Determine which one provides the best measurement uncertainty, i.e., in the reading result , and provide the value of the uncertainty found for that DVM. Assume that all of them provide the same reading .

The accuracy performance for each DVM is summarized below.

Consider a digital multimeter (DMM) operating as an ohmmeter.

The manufacturer specifies the accuracy performance of the ohmmeter as follows.

Assuming the resistance reading of , determine the minimum absolute value of the reading uncertainty.

Consider the measurement of the peak-to-peak voltage () of a periodic signal using a digital storage oscilloscope (DSO).

The DSO manufacturer specifies the vertical scale accuracy as of full scale in the basic measurements manual.

As with any measurement, values obtained directly from the oscilloscope screen, such as , are inherently associated with an uncertainty (). For the present case, determine in percentage (%).

A digital multimeter (DMM) is used as a voltmeter to measure the potential difference of between two terminals of a device under test (DUT). The measurement is performed at a location with a temperature of .

The dc voltmeter has a display of 3.75 digits and operates within voltage ranges of 400 mV, 4 V, and 40 V. The remaining specifications are shown below.

Determine the absolute value of the reading uncertainty.

Consider the dc voltage measurement shown in figure, in which a 3  digital multimeter (DMM) is used as dc voltmeter, measuring . Obtain the minimum absolute value of the uncertainty associated to this voltage reading, i.e. in the reading result .

The dc voltmeter accuracy performance is shown next.