# Consider the following simple R-2R resistor ladder implementation of a

Consider the following simple R-2R resistor ladder implementation of a 4-bit digital-to-analogue converter (DAC).
Each input d3, d2, d1 and d0 is independently driven from a corresponding digital output pin of a microcontroller. d3 is the most significant bit, d0 is the least significant bit.
Owing to the power supply of the microcontroller, each output delivers 4.8V for a logic 1 and 0V for a logic 0.
If d3 is [D], d2 is [C], d1 is [B] and d0 is [A], determine the output voltage Vout.
A filter is required to remove the switching frequency components from a PWM signal. The filter corner frequency is required to be 10kHz. The circuit is shown below. If R1=R3=R and C1=C2=C, specify a suitable value for C (as an absolute value in farads to 2 significant figures) if the minimum input impedance of the filter is to be 20k
Suppose you are prototyping a relay drive circuit as shown in the figure below
You do not have any diodes currently in stock for protecting the transistor, Q1. However, you do have a spare NPN transistor Q2.
As a short-term solution, how would you connect the transistor Q2 between points A and B to protect Q1?
The most satisfactory way of generating a reference voltage for an analog to digital converter is:
using a zener diode
using a band-gap reference
the output of a potential divider across the supply rails
connecting the reference pin directly to the supply.
The circuit below shows a relay driver controlled by an ATMega328 microprocessor. The supply voltage Vcc is 12V. The transistor Q1 has an hfe range of 90-6000 and the base-emitter voltage when saturated may be assumed to be 0.7 V. The relay coil requires a current of 1.75 A to stay pulled in.
Calculate the minimum value of R1 required to ensure the circuit will work across a production run. Your answer should be exact (not the nearest preferred value) and rounded to the nearest integer value.