There are only six types of tea! That is, only those processed from Camellia sinensis leaves can be called this way. All others, nicknamed herbal teas are in reality tisanes (infusions). Anyway, this exercise will lead you to part of the design of a temperature sensor that monitors temperature of tea brewing (and infusions as well) on the appropriate scale, as indicated in the next table.

Let us make use of a thermistor NTC with at and . Furthermore, assume margin for the temperature range of interest, i.e. 10 % below 70 °C and above 100 °C. Consider the following circuit.

Now, firstly consider the midrange temperature, let us call it and derive based on the inflection-point method, i.e. .

Then, design the remaining circuit obtaining the value of that implies an output at half the power supply when the temperature is at midrange, i.e. . Admit and a linear output voltage range limited to from the power rails, i.e. , which should coincide with the temperature range specified.

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 .

Consider the following Maxwell inductance bridge circuit used to characterize the inductance modeled as the self-inductance and its equivalent series resistance .

By properly adjusting the variable resistor  and the variable self-inductance , the bridge is kept in equilibrium at , i.e. .

Under these circumstances, .

As for the inductor , its equivalent series resistance is .

Estimate the ratio between the unloaded quality factors of the inductors and (without in ), i.e. .

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 the following circuit with a perfect bipolar analog-to-digital converter (ADC), with a uniform mid-tread quantizer, having a dynamic input range from to . Also, consider that, at the input , and the range of is .

Considering that has been designed to minimize the quantization error of the ADC in the full range of , obtain the output (in decimal) in the case where .

Consider the following circuit with a fully-differential amplifier (incorporating internal common-mode feedback) driving a perfect bipolar analog-to-digital converter (ADC). The ADC has bits.

The ADC operates with an input differential signal (as indicated in the figure) in all the dynamic range, i.e. the range of its power-supply from to , with . It also allows common-mode voltages within this range, but each signal and must be limited to this input range.

The differential signal is obtained from a sinusoidal voltage according to the gain that provides .

Assuming , obtain the signal-to-noise ratio, SNR(dB), at output of the converter.

Note: The ADC input filter circuitry only removes unwanted high-frequency noise, it does not affect the input signal.

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 8.3 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.