Consider an analog-to-digital converter (ADC) with the transfer function (mid-tread quantizer) shown in the figure.

Assuming the ADC with full-scale voltage , and assuming that the ADC has no imperfections of any kind, derive the value of the quantization step ().

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 .

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 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.

The measurement system depicted in the figure below consists of a resistive Wheatstone bridge excited by a dc current. To establish the excitation current in this configuration, a zener diode is employed, with . The zener is considered here as an ideal device, operating in regulation with a current through its terminals of 5.3 mA.

Assume , , , . In the Wheatstone bridge consider and  mΩ/Ω.

Determine the common-voltage at the bridge output (i.e., the common-mode voltage of and ).

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 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.

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.

The following measurement system is designed to obtain the root mean square (RMS) voltage of sine waves without any dc component, such as .

The first stage operates as a full-wave rectifier with gain , as shown in the input-output characteristic in the figure below. The second stage consists of an averaging circuit with gain .

Assuming , determine such that the output voltage corresponds to the RMS value of the input signal .