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., ).

The temperature of an industrial boiler is monitorized by means of a J-type thermocouple with a hot-junction temperature and a cold-junction temperature of .

Under the present conditions, assuming an ideal operational amplifier, obtain the output voltage of the circuit () in which and .

The Maxwell inductance bridge shown in the figure was used to characterize the inductance under test, modeled as the self-inductance and the respective equivalent series resistance .

The bridge achieves equilibrium by adjusting the variable resistor  and the variable self-inductance . The resultant values for these components are and .

The standard resistances have values and , and for inductor , its equivalent series resistance is .

Calculate the self-inductance .

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?

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.

Consider a bits bipolar ADC (rail-to-rail, ) in which the measured signal to noise-and-distorion ratio (SINAD) is for an input signal , where is much lower than the sampling frequency (the RC filter does not affect the signal, it only removes high-frequency noise, avoids aliasing) and .

Determine the effective number of bits (ENOB) of the ADC.

Consider the subranging -bit half-flash ADC shown in the figure (the ADCs employ uniform mid-rise quantizers). All the components are ideal, including rail-to-rail inputs/outputs with . The only exception is in the DAC output offset, which due to a fabrication error is .

For a sampled input voltage of , determine the digital output in 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 4.8 mA.

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.