# PHYS1101 Physics I

## Question:

Take a look at the simple R-2R resistor ladder installation of a 4-bit digital to analogue converter (DAC).

Each input d3,, d2, d1 or d0 is driven independently from the corresponding digital output pins of a microcontroller.

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d3 represents the most important bit, while d0 represents the least.

The microcontroller provides a power supply that delivers 4.8V to a logic 1 output and 0V to a logic 0.

The output voltage Vout is determined if d3 and d2 are [C], d1 and d0 are [A], respectively.

A filter is needed to remove the switching frequencies components from a PWM signals.

The filter corner frequency should be 10kHz.

The circuit is as follows.

If R1=R3=R, and C1=C2=C1, specify the appropriate value for C (as an Absolute Value in farads up to 2 significant numbers) if the minimum input resistance of the filter is to reach 20k

Let’s say you are prototyping the relay drive circuit shown in this figure.

For protecting the transistor, you don’t have any diodes available at this time Q1.

However, you do own a spare NPN-transistor Q2.

What is the best way to connect Q2 between points A & B, in order to protect Q1 as a short-term solution?

The best method to generate a reference for an analog converter to digital converter is:

Referring to a band gap reference

Potential dividers output across the supply rails

Connect the reference pin to the supply directly

This circuit shows an ATMega328 microprocessor controlling the relay driver.

The supply voltage Vcc runs at 12V.

The transistor Q1’s hfe range is 90-6000. The base-emitter voltage, when saturated, may be assumed as 0.7 V. To keep the relay coil in place, it requires a current to 1.75 A.

Calculate the minimum value R1 needed to ensure that the circuit is functional across a production run.

Here is an example of a 4-bit DAC conversion implemented using a simple R-2R resistor ladder.

The output voltage V0 is expressed as follows:

Here N = 4, as the digital input for this example is 4-bit.

Vref = (given) 4.8 volts

Rf = 0?

(since there is no resistance in the negative feedback of an op-amp.

R1 = 20 k (the resistance that is connected to the ground)

Therefore, the analogous output voltage V0 of this circuit for the given digital inputs are 55.2 volts.

The cut-off frequency of the lowpass filter is 10 KHz.

The filter accepts all signals below the corner frequency.

Therefore, the filter permits all signals below this corner frequency.

This particular filter is the Second Order Twofold-Gain SallenKey Low-Pass.

The input impedance for the filter’s s-domain is given as by

Recognizing that R1=R2=R, and C1=C2=R.

Therefore, the input impedance equation becomes.

For a given R value, the value C can be calculated from equation (1).

Below is the 2-diode NPN transistor design.

This two-diode version of the transistor Q2 is now compatible with the terminals B and A.

The +12V line will connect the emitter of Q2 to the collector of Q1 transistor.

The relay switches connect the base of Q1 transistor to the relay switches.

When the emitter voltage is greater than the base voltage, current flows to Q1’s collector.

Therefore, Q1 protects itself from current flowing directly from the +12V supply.

The reference voltage refers to the maximum voltage that can convert from Analog to digital.

The supply should have some resistance in order to produce the reference voltage. This is the maximum voltage that can convert from Analog to its equivalent digital value.

Zener diode can permit current to flow in reverse so that the A/D converts the Analog voltage to the digital equivalent.

The best method to generate the reference voltage for an Analog converter to digital converter is by using a Zener Diode.

Given that Vcc = 12 V, the supply voltage.

When transistor Q1 is saturated, the base-emitter current is 0.7 V.

The minimum value of current that is required to work the circuit during production run (i.e.

1.75 Amps is the minimum current needed to ensure that the relay coil stays pulled in.

Accordingly, the minimum current required to flow across R1 must be 1.75 A.

Voltage (base Q1) = 0.7 volts

Therefore, 6 is the minimum value for R1 to ensure the circuit will function across a production run.

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