Consider the circuit shown with a K-type thermocouple, with Seebeck coefficient , used to sense the temperature in a oven.

Assuming the operation amplifier as rail-to-rail output, obtain the value of in the circuit so that the difference between the oven temperature () and the cold junction temperature ( is maximized in the interval .

In order to characterize a capacitor at , both and were adjusted to achieve equilibrium on the Schering bridge shown below. The capacitor to be characterized is modeled by its capacitance value and equivalent series resistance .

Under bridge equilibrium conditions, and . The standard fixed-value components are and .

Determine the dissipation factor (loss tangent, ) of the capacitor to be characterized.

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.

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

A sinusoidal waveform has been obtained at a new frequency , thus . Find the value of the resultant signal .

Consider the -bit successive-approximation register (SAR) analog-to-digital converter (ADC) with full-scale voltage and internal clock frequency (SAR logic) of , faster than the sampling frequency (). Each comparison takes clock cycles.

Find the conversion time for an input voltage of .

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 1.1 mA.

In the following circuit, in which the amplifier is assumed ideal, the input () can operate between voltages and .

Assume that the output of the amplifier () will drive a circuit with input range between and , and . The resistance is and .

Determine to satisfy the maximum dynamic range requirement.

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.