2. Lecture 4
AC Electronics
DC vs. AC
All the currents and voltages we have worked with so far are constant positive
voltage and DC (Direct Current). Power and signals are often delivered using
an oscillating current that changes direction, AC (Alternating Current) and
voltage that changes from positive to negative.
Mains voltage is delivered at 230V AC in this country. When this is generated
at the power station, the generating motors’ magnets produce power in AC
form, and it is then easy to convert between voltages through transformers to
the home.
Analogue signals are modulated on to radio frequency (RF) AC for
transmission. In Amplitude Modulation (AM) radio for example the amplitude
of the wave is changed to carry the information.
Waveform
The AC voltage or current can be viewed as a sine wave (the solid line):
Amplitude
sine cosine
A P
Time
T
Where:
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3. A is the amplitude of the waveform. It is measured from zero to the
peak of the wave.
P is the peak-to-peak (p-p) amplitude. It is measured from the peak to
the trough of the wave.
T is the time period of the wave – the time it takes for the wave to go
through one cycle.
The dashed line in the waveform diagram above is a cosine wave. The
difference in starting points of the waves is a phase difference, and is
measured in seconds, or sometimes in degrees (°) where one cycle is 360°.
What is the phase difference in degrees between sine and cosine?
Other Types of Waveforms
Frequency Domain
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4. A useful way of representing AC signals is in the frequency domain, instead
of the time domain, for example for viewing the spectrum of a signal with a
spectrometer. In this domain the Y-axis represents the voltage gain and the
X-axis the frequency.
The frequency of an AC signal is directly related to the period of the wave:
Where:
f is the frequency in Hertz (Hz)
T is the time period of one wave in seconds
In the frequency domain, the X and Y axes are both log scales (logarithmic)
where an equal division represents an increase of x10. The gain is measured
in decibels (dB) and is found using the log function:
Where:
G is the gain in decibels (dB)
Vout is the amplitude of the output in Volts
Vin is the amplitude of the input in Volts
Gain
G
Frequency
Draw a 1kHz sine wave on the above graph, where Vout = Vin.
What is the time period of this wave?
Filters
Lecture 4: AC Electronics
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5. In order to isolate AC signals, it is necessary to filter out areas of the
spectrum. There are three main types of filters:
• LPF (Low-Pass Filter). Allows low frequencies to pass, but filters high
frequencies.
• HPF (High-Pass Filter). Allows high frequencies to pass, but filters low
frequencies.
• BPF (Band-Pass Filter). Allows a mid-band of frequencies to pass, but
filters lower frequencies and higher frequencies.
An ideal filter would provide a sharp cut-off at the required frequency, but
realistically filters have a roll-off. The point at which the filter has a gain of
-3dBs is the -3dB frequency, f-3dB, and is used to describe the filter.
Gain
(dB) 0
-3
Roll-off
f-3dB
Frequency (Hz)
What is the percentage of Vout / Vin at a gain of -3dBs?
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6. Draw the frequency responses of the other types of filters
and mark the -3db frequency(s):
HPF
Gain
Frequency
BPF
Gain
Frequency
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7. RC Filters
The simplest kind of filter is constructed from a single resistor and capacitor.
In the low pass filter configuration:
R
C
Vin Vout
From capacitor theory we know that the time constant for this RC combination
is:
Where:
τ, (‘tau’) is the time constant in seconds
R is the resistance in Ohms
C is the capacitance in Farads
The resistor and capacitor combine to make a filter, and the -3dB point of the
filter can be found from the time constant:
What is the capacitance in a RC Low Pass Filter with resistance 1k
and a -3dB frequency of 3.4kHz?
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8. Practical: Build an RC Filter
Read the Health and Safety Information on page 5.
• Build the following circuit:
R
C
Vin Vout
Use a signal generator for the AC source, Vin and an oscilloscope
to measure Vout.
• Draw the frequency response of your filter.
• Calculate the -3dB frequency. How does this compare with your
measurements?
Extended Practical: Other RC Filters
• Repeat the above practical for a High Pass Filter, where the
capacitor and resistor are swapped over.
• Design a bandpass filter with two stages, one LPF and one HPF.
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9. Health & Safety Considerations
Soldering and de-soldering:
Solder melts at between 180 and 200°C. Soldering irons will heat up to
between 250 and 400°C. Be extremely careful when soldering and take the
following precautions:
• Switch off the soldering iron at the mains when not in use
• Always keep the iron in its stand
• Make sure your workspace is clear, well lit and well ventilated
• Never solder while your circuit is powered up
• Never solder without tutor supervision
• Only apply the soldering iron for the minimum amount of time
• Keep your soldering tidy and use the minimum amount of solder
• Avoid breathing in solder fumes
• You must only use the lead-free solder provided
• You must use tools e.g. pliers to support components that are
being soldered and ensure the board is secure.
Switching it on:
Powering up a circuit that is incorrectly connected can cause components or
equipment to get extremely hot or even ‘blow’. A short circuit (where
unintended electrical connections are made) for example may damage
equipment or blow components causing them to behave in an unpredictable
way.
• Before powering up your circuit you MUST have it checked by the
tutor
• Have your neighbour physically inspect your work before
powering on
• If your circuit does not behave as you expect, switch it off
immediately
• Use your nose! A faulty circuit with hot components will often
smell or smoke
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10. If your circuit does not behave as you expect:
• With the power off, confirm by eye that your circuit is connected
correctly and that you are using all the correct components and
mounted with the correct polarities
• Inspect your circuit closely for short circuits, soldering faults and
dry joints:
• Do all the testing on your circuit that you can with it powered off.
• Be extremely careful when probing your circuit live as the probe
itself can cause short circuits
• When probing with an oscilloscope ensure the earth connection is
applied safely
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