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 .

The spectral components (magnitude) of two signals is shown below.

In the circuit obtain V_x assuming that the RMS value of the current in the resistor is 2.6 mA.

Consider a remote measurement conducted over long distance, where each wire has a total resistance of , sharing identical lengths.

Admitting the instrumentation amplifier (IA) gain given by , with gain resistor , obtain the output voltage when .

The measurement system depicted in the figure below consists of a resistive Wheatstone bridge excited by a dc current. To establish the excitation current in this configuration, a zener diode is employed, with . The zener is considered here as an ideal device, operating in regulation with a current through its terminals of 5.3 mA.

Assume , , , . In the Wheatstone bridge consider and  mΩ/Ω.

Determine the common-voltage at the bridge output (i.e., the common-mode voltage of and ).

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 (%).

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.

Consider the temperature measurement circuit depicted in the figure, which uses a thermistor as the temperature sensor, i.e. the resistor with negative temperature coefficient (NTC). The temperature operating range is from 0 °C to 100 °C.

Also, admit the sensor characteristic, which is shown in the next figure, being defined by a constant over the operating temperature range.

The circuit is designed to minimimze the common-mode voltage at the amplifier inputs at midscale temperature. Consider and obtain the value of that uses the maximum analog-to-digital (ADC) dynamic range.

Consider an extruder of a 3D printer with temperature control provided by a K-type thermocouple transducer with Seebeck coefficient . At the cold junction it is used an analog integrated-circuit temperature sensor with lower temperature range, but suitable for measuring the thermal block temperature. It provides cold-junction compensation by means of a proportional-to-absolute temperature (PTAT) voltage , which drives the instrumentation amplifier (IA) reference pin (voltage/temperature characteristic shown in figure). The IA output voltage consists of .

What is the maximum temperature (in °C) that can be measured at the extruder given a maximum linear IA output voltage of ?

Consider the following Hay bridge for inductance measurements.

Suppose that and were adjusted ( and ) to achieve bridge equilibrium at , i.e., .

The standard fixed-value components are and .

Determine the value of the inductor, .

The universal digital counter, with the simplified diagram representation shown below, is operating as a frequency meter. The oscilator frequency is and the decade divider provides the time-base selection of frequency signals , .

Assuming an input signal with frequency , what is the number of pulses obtained by the decade counter when the most adequate time base has been chosen?