For the Maxwell-Wien bridge shown in the figure in equilibrium (null detection between terminals and ) the values of the variable components are and . The fixed-value components are and .

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 worst than a perfect ADC. The input signal , where is much lower than half the sampling frequency, and .

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

Consider a differential sinusoidal signal driving a perfect bipolar analog-to-digital converter (ADC), with a uniform mid-tread quantizer. The differential signal at the input of the ADC, , covers the complete input dynamic range of the ADC, from to . The ADC input filtering only removes unwanted high-frequency noise, it does not affect the input signal. At the output of the ADC, the signal to quantization noise ratio is .

Admiting the quantization noise power of , determine the quantization step ().

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 6.1 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 .

Consider the following circuit where the node represents the low-impedance output of a sensor, with a linear operating range of .

The requirement is to convert this input voltage range to an output voltage range of . Determine the most suitable value for the Zener voltage.

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.