Consider the following digital-to-analog converter (DAC), which uses a 3-bit word () to control which of the switches turns on (’1’ means closed) while all the others are kept turned off (’0’ means opened). For this end, it uses a decoder that converts each input to a 8-bit word () by means of one-hot encoding (only a single bit is ’1’).

Assuming the reference voltage , what is the analog output voltage for a binary input 101.

A single tone , where , has been sampled by an analog-to-digital converter (ADC) at the sampling frequency .

A sine wave has been obtained at new frequency (). Determine the frequency value of of the resulting tone .

Consider the following transfer function of a perfect bipolar analog-to-digital converter (ADC), with a uniform mid-tread quantizer, in which the input value shown is .

For an input of , obtain the digital output in two’s complement binary.

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 4.2 mA.

Consider the following voltage amplification circuit in which a Wheatstone bridge is employed at the input of an instrumentation amplifier (IA).

Assume , , , and .

Determine the value of so that the differential component has a low-pass filter response with cut-off frequency at 10 Hz (assume ).

Consider the following voltage reading in which the nominal closed-loop voltage gain of the (ideal) operational amplifier is and the dc output voltage is .

Both resistors are rated at , composed by metal film with thermal coefficients and thermal resistances .

The analog-to-digital converter is unipolar, rail-to-rail input, has bits, and can be assumed perfect.

Determine the minimum nominal value of the resistor for which the gain error is imperceptible.

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 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.

The following circuit is used as a thermostat. When the temperature rises above a critical value (), the comparator output goes high, indicating overtemperature.

The circuit employs an NTC thermistor () for temperature sensing, with at 25 °C and , assumed constant for all the temperature range.

Determine the temperature (in °C) at which the comparator changes its output value (i.e., ).