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Circuit Surgery
Regular clinic by Ian Bell
Frequency Shifting and Superheterodyne Receivers – Part 2
𝑆𝑆! = 𝐴𝐴! cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡)
Frequency shifting and superheterodyne receivers – Part 2
L
ast month, we started looking
𝑠𝑠"# = 𝐴𝐴$ (1 + 𝑘𝑘𝑆𝑆# )
a sinusoidal message of amplitude AM
two input frequencies (two sinusoid
at superheterodyne radio receivinputs) multipliers output just the sum
the modulation depth is:
ers, mainly concentrating on the
and difference frequencies, whereas with
𝑘𝑘𝐴𝐴#
principles of heterodyning (frequency
other nonlinear circuits there may also be
𝑚𝑚 =
× 100%
𝐴𝐴!
shifting) and the mixers that provide
many other output frequencies. We often
this function. This month, we will
only want one of the sum or difference
look at the structure and operation of
frequencies, so we have to filter the
The maximum modulation depth
superheterodyne radio receivers in
mixer output to remove the unwanted
without causing distortion is 100%,
𝑆𝑆# = 𝐴𝐴#that
cos(2𝜋𝜋𝑓𝑓
more detail.
signals. Multiplier
circuits
require
a
beyond
we have
overmodulation.
# 𝑡𝑡)
Frequency Shifting and Superheterodyne
Receivers
– Part
2
Radio transmission systems are
relatively large number
of
transistors
Real
AM
voice/music
radio
systems
Frequency
Shifting
and Superheterodyne
Receivers
– Part
Frequency
Shifting
and Superheterodyne
Receivers
– Part
2 2
fundamentally based on heterodyning.
to implement so are more commonly
have modulation depths well below this,
Superheterodyne
Receivers
– Part
The signal to be transmitted, referred
found on Frequency
integratedShifting
circuitand
receivers.
maybe
to 60%
in2sinewave terms,
𝑆𝑆! = 𝐴𝐴30%
! cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡)
to as the message signal, (for example,
The nonlinearity of a single transistor
because
real
signals
do
𝑠𝑠"# = 𝐴𝐴$ (1but
+ 𝑘𝑘𝐴𝐴
cos(2𝜋𝜋𝜋𝜋
𝑡𝑡))
cos(2𝜋𝜋𝜋𝜋
%
$ 𝑡𝑡)not have
𝐴𝐴! cos(2𝜋𝜋𝑓𝑓
𝑆𝑆! =𝑆𝑆%
𝐴𝐴
! !=cos(2𝜋𝜋𝑓𝑓
! 𝑡𝑡) ! 𝑡𝑡)
speech) is upshifted from its original
or diode (or tube/valve in the old days)
constant amplitude their modulation
cos(2𝜋𝜋𝑓𝑓
frequency range (called the baseband)
can be used for mixing in circuits with 𝑆𝑆depth
expressed
in rms (root mean
! = 𝐴𝐴! is
! 𝑡𝑡)
to the much higher frequencies
a relatively low component count.
square) terms, where the typical values
𝑠𝑠"# = 𝐴𝐴$ (1 + 𝑘𝑘𝑆𝑆# )
(radio frequencies – RF) required
may
the
20%
to 40%
𝑠𝑠"# = 𝐴𝐴! cos(2𝜋𝜋𝑓𝑓
+ in
𝑘𝑘𝐴𝐴𝑠𝑠%
cos(2𝜋𝜋𝜋𝜋
𝑡𝑡)
! 𝑡𝑡)be
$𝐴𝐴
# 𝑡𝑡) rms
(1
𝑠𝑠range
(1
𝐴𝐴 =
+$ cos(2𝜋𝜋𝑓𝑓
𝑘𝑘𝑆𝑆+
"#
"# =
# )𝑘𝑘𝑆𝑆# )
for practical wireless transmission
(for example,
see$ the International
Amplitude modulation
= 𝐴𝐴$ (1 + 𝑘𝑘𝑆𝑆# )
of electromagnetic signals. This is
Telecommunications
Union report
Superheterodyne receivers can be used 𝑠𝑠"#
achieved by varying (modulating) one or
ITU-R BS.2433-0 (10/2018)).
with a variety of modulation schemes,
𝑘𝑘𝐴𝐴#
more properties of an RF carrier signal
but we will just refer to amplitude
𝑚𝑚 =
× 100%
𝑘𝑘𝐴𝐴# 𝑘𝑘𝐴𝐴#
𝐴𝐴!
× 100%
in sympathy with the message signal.
modulation (AM) in this article to keep
AM signals
𝑚𝑚 =𝑚𝑚 = × 100%
𝐴𝐴message
! 𝐴𝐴!
A radio receiver must then downshift
things simple. Before discussing the
For a𝑘𝑘𝐴𝐴sinusoidal
at frequency
#
𝑚𝑚 =
× 100%
the signal from the RF carrier frequency
receiver, it is worth looking at AM
fM and
𝐴𝐴!amplitude AM, that is given by:
to the original baseband to recover
signals, so we know what the receiver
𝑆𝑆# = 𝐴𝐴# cos(2𝜋𝜋𝑓𝑓# 𝑡𝑡)
the message, which is referred to as
is dealing with. As the name suggests
𝐴𝐴# cos(2𝜋𝜋𝑓𝑓
𝑆𝑆# =𝑆𝑆#
𝐴𝐴#=cos(2𝜋𝜋𝑓𝑓
# 𝑡𝑡) # 𝑡𝑡)
demodulation or detection.
amplitude modulation involves
changing the amplitude of a fixed 𝑆𝑆#The
modulated signal, using
= 𝐴𝐴resulting
# cos(2𝜋𝜋𝑓𝑓# 𝑡𝑡)
frequency carrier wave in proportion
the equation above, is:
Mixer recap
𝑠𝑠"# = 𝐴𝐴$ (1 + 𝑘𝑘𝐴𝐴% cos(2𝜋𝜋𝜋𝜋% 𝑡𝑡)) cos(2𝜋𝜋𝜋𝜋$ 𝑡𝑡)
to the message signal. The carrier signal
The principle of the superheterodyne
𝑠𝑠"#
𝑡𝑡)) cos(2𝜋𝜋𝜋𝜋
(1𝐴𝐴+$ (1
𝑠𝑠"# =
𝐴𝐴$=
𝑘𝑘𝐴𝐴+%𝑘𝑘𝐴𝐴
cos(2𝜋𝜋𝜋𝜋
cos(2𝜋𝜋𝜋𝜋
% cos(2𝜋𝜋𝜋𝜋
% 𝑡𝑡))%
$ 𝑡𝑡) $ 𝑡𝑡)
(SC) is a high-frequency
receiver is downconversion
a fixed
Frequency Shiftingtoand
Superheterodyne
Receivers – Part 2(RF) sinusoid
intermediate frequency (IF) before
at frequency fC and amplitude A𝑠𝑠C, which
"# = 𝐴𝐴$ (1 + 𝑘𝑘𝐴𝐴% cos(2𝜋𝜋𝜋𝜋% 𝑡𝑡)) cos(2𝜋𝜋𝜋𝜋$ 𝑡𝑡)
further downcoversion to the baseband.
we can write as:
Multiplying out:
𝑠𝑠"# = 𝐴𝐴! cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡) + 𝑘𝑘𝐴𝐴% cos(2𝜋𝜋𝜋𝜋$ 𝑡𝑡) cos(2𝜋𝜋𝑓𝑓# 𝑡𝑡)
The intermediate frequency used in
𝑆𝑆! = 𝐴𝐴! cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡)
𝑠𝑠"#
𝐴𝐴! cos(2𝜋𝜋𝑓𝑓
𝑠𝑠"# =
𝐴𝐴!=cos(2𝜋𝜋𝑓𝑓
𝑘𝑘𝐴𝐴+%𝑘𝑘𝐴𝐴
cos(2𝜋𝜋𝜋𝜋
! 𝑡𝑡)
% cos(2𝜋𝜋𝜋𝜋
$ 𝑡𝑡) cos(2𝜋𝜋𝑓𝑓
! 𝑡𝑡) +
$ 𝑡𝑡) cos(2𝜋𝜋𝑓𝑓
# 𝑡𝑡) # 𝑡𝑡)
superheterodyne receivers is at a much
higher frequency than audio (hence
Note that the 2π factor converts
𝑠𝑠"# = 𝐴𝐴! the
cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡) + 𝑘𝑘𝐴𝐴% cos(2𝜋𝜋𝜋𝜋$ 𝑡𝑡) cos(2𝜋𝜋𝑓𝑓# 𝑡𝑡)
the ‘super’ part of the name). The fact
ordinary frequency of the signal (fC) in
Frequency Shifting and Superheterodyne Receivers – Part 2
that the IF is a fixed frequency makes
hertz
angular frequency (w) in
The signal is equivalent to the carrier plus
𝑠𝑠"# =to𝐴𝐴an
$ (1 + 𝑘𝑘𝑆𝑆# )
the design of a receiver with good
radians. The message signal (SM) is at
the carrier multiplied by the message.
performance much easier than if most
Based on this and using a similar approach
a lower frequency (for example, audio)
𝑆𝑆! = 𝐴𝐴! cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡)
of the circuitry has to cope with (be
and
varies the instantaneous amplitude
tuneable to) the full range of carrier
of the 𝑘𝑘𝐴𝐴
carrier to give the modulated
#
𝑚𝑚 = (SAM×
frequencies which need to be received.
signal
): 100%
𝐴𝐴!
Heterodyning is achieved using
𝑠𝑠"# = 𝐴𝐴$ (1 + 𝑘𝑘𝑆𝑆# )
Introduction to LTspice
mixers. These are nonlinear circuits
that combine signals to produce new
Want to learn the basics of LTspice?
frequencies (heterodynes) not present
In this expression, k is the modulating
Ian Bell wrote an excellent series of
𝑆𝑆# = 𝐴𝐴which
# cos(2𝜋𝜋𝑓𝑓
Circuit Surgery articles to get you up
in the input. We discussed mixers in
factor,
is #a𝑡𝑡)value greater than
𝑘𝑘𝐴𝐴#
and running, see PE October 2018
detail last month. To recap briefly, an
zero.
of k, together with the
𝑚𝑚 =The value
× 100%
to January 2019, and July/August
ideal mixer multiplies two signals,
relative𝐴𝐴!amplitudes of carrier and
2020. All issues are available in
but if signals are combined (added)
message determine the modulation
print and PDF from the PE website:
𝑠𝑠"# = 𝐴𝐴$ (1
+ 𝑘𝑘𝐴𝐴(m),
% cos(2𝜋𝜋𝜋𝜋
$ 𝑡𝑡)
and applied to any nonlinear circuit
depth
that %
is𝑡𝑡))
thecos(2𝜋𝜋𝜋𝜋
amplitude
of the
https://bit.ly/pe-backissues
then heterodyning will occur. With
modulation relative to the carrier. For
𝑆𝑆# = 𝐴𝐴# cos(2𝜋𝜋𝑓𝑓# 𝑡𝑡)
48
Practical Electronics | January | 2024
𝑠𝑠"# = 𝐴𝐴! cos(2𝜋𝜋𝑓𝑓! 𝑡𝑡) + 𝑘𝑘𝐴𝐴% cos(2𝜋𝜋𝜋𝜋$ 𝑡𝑡) cos(2𝜋𝜋𝑓𝑓# 𝑡𝑡)
Fig.1. LTspice schematic for behavioural simulation of amplitude modulation.
Fig.4. LTspice modulator special
function component.
is the same as in Fig.3. If there is no DC
offset on the AM input the modulator
component (configured for AM) will
act as a multiplying mixer.
Sidebands
Fig.2. Waveform results from the circuit in Fig.1 with k = 0.3 (30%).
to that used for mixers last month, we can
create an LTspice behavioural simulation
of amplitude modulation (see Fig.1). Like
last month, to make it easier to see both
the carrier and message waveforms, we
are not using typical radio frequencies
for the carrier. In the example the value
of the modulation factor (k) is set up as
a parameter.
Fig.2 shows the results from the
simulation in Fig.1 for k = 0.3 (30%).
Fig.3 shows the modulated waveform
for k = 0.6 (60%). As mentioned last
month, when considering the operation
of radio systems, we are often more
interested in the signal spectra rather
than the waveforms in the time domain.
Therefore, the simulation is again
configured to facilitate viewing of the
spectrum with LTspice’s FFT function.
In the circuit in Fig.1, we used a
behavioural source to implement an AM
modulator. An alternative approach is
to use the ideal modulator component
that is available in LTspice. This can be
found in the ‘Special Functions’ folder of
the component selector. It provides both
amplitude and frequency modulation
(AM and FM) functionality. It has two
parameters – mark and space – which
set the upper and lower FM frequencies.
These should be the set to the same
value, equal to the carrier frequency,
for AM. An example circuit with the
modulator component configured for
AM is shown in Fig.4. The example
uses a 0.6V-amplitude sinewave message
signal on a 1.0V DC offset, with a 20kHz
carrier signal. This produces AM with
60% modulation depth, so the output
Fig.3. Waveform results from the circuit in Fig.1 with k = 0.6 (60%).
Practical Electronics | January | 2024
From the discussion on mixers last
month, we know that the multiply
term in the equation for AM with
sinusoids given above will produce
an output with two signals at the sum
and difference frequencies (f C – f M )
and (f C + f M), the carrier term in the
equation means that this frequency
(f C ) will also be present in the AM
modulator output. This is shown in
Fig.5, which is the spectrum (LTspice
FFT) for the modulation waveform
from the circuit in Fig.1, where the
sum (20 + 2 = 22kHz) and difference
(20 – 2 = 18kHz) and carrier (20kHz)
peaks can be seen.
In the context of modulation, sum
and difference frequencies are referred
to as the upper and lower sidebands
respectively. They are single frequencies
in this LTspice example, but in general
they comprise the full message bandwidth
upshifted to ranges above and below the
carrier frequency. This is illustrated in
Fig.6. The spectrum on the left of Fig.6
is the baseband and comprises a range of
relatively low frequencies (from fm,min to
fm,max); for example, audio from a few tens
of hertz to several kilohertz. Like Fig.4,
the frequency axis is linear and includes
zero frequency (DC) unlike the logarithmic
scales commonly used for plots such as
amplifier frequency responses.
The right of Fig.6 shows the spectrum
of the AM signal produced by using the
baseband signal on the left to modulate
a carrier of frequency fC. The baseband
is upshifted to the sum and difference
frequencies and so appears both above
and below the carrier frequency as the
upper and lower sidebands. Note the
‘reversal’ of the lower sideband – the
highest baseband frequency is shifted
to the lowest frequency in the lower
sideband. The gap between the carrier
and sidebands on both sides is equal
to the lowest baseband frequency. The
plots in Fig.5 are not to scale – the
49
Fig.5. Spectrum of the modulated waveform of the circuit in Fig.1 with k = 0.6 (60%).
break in the AM plot axis indicates
that a typical carrier frequency is much
further along the axis (relative to the
size of the sidebands) than where it is
located in the drawing.
The full AM signal takes more
bandwidth and power to transmit than
is strictly necessary. For normal AM
the sidebands are symmetric (see Fig.6),
so only one needs to be transmitted,
halving the bandwidth – this is called
Single Sideband (SSB). The carrier
contains no message information, so can
be reduced in amplitude or removed
(referred to as suppressed carrier),
which can be applied to both single and
double sidebands (SSB-SC and DSBSC). Not transmitting a sideband and/or
the carrier reduces power requirements
or increases coverage with the same
power. Receiving SSB and suppressed
carrier signals is more complex and
requires higher receiver performance
Intermediate frequency
As previously explained, a key feature
of the superheterodyne receiver is the
downshifting of the received signal to a
fixed intermediate frequency. The idea
of what is required is illustrated in Fig.7.
There is a range of possible received
signals, that is different carrier signals
and their associated sidebands from the
various stations or channels that can
be received. One of these is selected
(by tuning to that station or selecting
that channel) and it is downshifted to
the fixed IF. The downshifting does not
change the shape of the spectrum of the
AM signal – it just shifts it to a new
centre frequency (fIF instead of fC). The
AM signal
Magnitude
Magnitude
Message (baseband)
than full AM, so is generally avoided
for commercial AM stations, but is
used in other contexts. For simplicity,
we will assume full AM signals when
discussing receivers here.
Carrier
Lower
sideband
fm,min
Message
bandwidth
f
fm,max
fm,min
fc – fm,max
Upper
sideband
fc
f
AM bandwidth
fc + fm,max
Fig.6. Signal spectra for AM.
Magnitude
Wide range of possible
received AM signals
Magnitude
0
0
fc,min
f
Selected AM signal
shifted to fixed IF
fIF
Fig.7. Shifting a received AM signal to IF.
50
fc,max
IF AM signal can then be demodulated
to recover the message signal.
As we know from the detailed
discussion of mixing last month,
shifting to IF can be achieved by mixing
(ideally multiplying) the received signal
by a sinusoidal signal at an appropriate
frequency. In a receiver, this signal is
generated by a local oscillator (LO).
The mixer produces sum and difference
frequencies, which means that either
the sum or difference frequency of the
received carrier with respect to the LO
frequency must match the required
intermediate frequency. Using a local
oscillator frequency below the carrier
frequency is called ‘low-side injection’;
if the local oscillator frequency is above
the carrier frequency it is ‘high-side
injection’. Both can be used, but for
basic AM high-side injection is more
common. The multiple frequencies
produced by nonlinear mixers are more
likely to produce disruptive signals in
the received signal range if low-side
injection is used.
Mixing the received carrier at fC with a
high-side local oscillator at fLO produces
signals at (fLO – fC) and (fLO + fC), with
their sidebands. Assuming we want
an IF which is lower than the carrier
frequency (it does not have to be) we
need fIF = fLO – fC. This means we need
to tune the local oscillator to fLO = fC +
fIF. We need the local oscillator to be
able to tune to fC + fIF throughout the
range of frequencies we want to receive.
In addition to the required IF signal at
f LO – f C the mixer will also produces
a higher frequency signal at fLO + f C.
This needs to be removed by filtering.
As a round-number example, for a
carrier range of 1.0MHz to 1.5MHz and
an IF of 400kHz (0.4MHz) the local
oscillator needs to tune from 1.4MHz
(1.0 + 0.4 = 1.4) to 1.9MHz (1.5 + 0.4
= 1.9). The mixer will also produce
signals in the range 2.4MHz (1.0 + 1.4 =
2.4) to 3.4MHz (1.5 + 1.9 = 3.4), which
need to be filtered out. This example
is similar to traditional broadcast AM
receivers where an IF of 455kHz was
commonly used (from the early days of
widespread superhet use). An advantage
of high-side injection is that a smaller
LO tuning range (ratio of highest to
lowest LO frequency) is required
than for low-side injection, which
makes things easier if the tuning is
implemented with a variable capacitor.
IF mixer simulation
fc
f
We can simulate the IF mixing in
LTspice by adding a LO signal and
behavioural multiplying mixer to the
circuit in Fig.1. This is shown in Fig.8 –
the carrier (from source V1) is at a higher
frequency (80kHz) than in the circuit
Practical Electronics | January | 2024
Fig.8. LTspice schematic for behavioural simulation of shifting an AM signal to an
intermediate frequency (IF).
in Fig.1, but the modulated signal
generation is essentially the same. The
modulated signal (signal modulated
from source B 1 ) is multiplied by
a 110kHz sinewave from the local
oscillator (LO signal from source V3)
using behavioural source B 2 . This
produces the intermediate frequency
Fig.9. Waveform results from the circuit in Fig.8.
output (signal IF) at 30kHz (fIF = fLO
– fC = 110kHz – 80kHz = 30kHz). The
schematic includes a filter which we
will discuss later.
The results of simulating the circuit
in Fig.8 up to the IF mixer output are
shown in Fig.9. The top three traces
(carrier (80kHz), message (2kHz) and
AM modulated signal) are similar to
Fig.2, but the carrier frequency is higher,
and the waveforms are zoomed in more.
The fourth trace is the local oscillator
(LO) at 110kHz. The bottom trace is
the IF signal from the mixer. This has
a complex-looking waveform, which
is difficult to interpret from its shape.
It is more useful to look at the spectra.
Fig.10 shows the spectra of the
modulated and IF waveforms from Fig.8.
It can be seen that the AM waveform
comprises the carrier (80kHz) and the
two sidebands (at 78kHz and 82kHz),
corresponding with Fig.5 and Fig.6,
as discussed earlier. The IF spectrum
shows the presence of two ‘AM’ signals
of equal amplitudes, one centred on
30kHz and the other on 190kHz. This
is the required IF signal centred on
30kHz and the additional signal from
the mixer centred on fLO + fC = 110kHz +
80kHz = 190kHz. Unlike the waveform,
the spectrum clearly shows that the IF
signal is behaving as expected from
mixing (ideal multiplying) the local
oscillator and AM signal.
Looking at the lower trace in Fig.10
we see that to obtain the desired signal,
that is the AM signal centred at the IF
frequency of 30kHz on its own, we need
to filter the IF mixer output to remove
the component of the waveform centred
at 190kHz. In this simplified example
there are no other signals present in the
spectrum, but in general the IF mixer
output spectrum will contain many
other significant peaks. These will
include the result of mixing signals
from adjacent radio stations/channels
with the local oscillator, and additional
spectral components resulting from
non-ideal mixer behaviour (see last
month’s discussion). Thus, a bandpass
filter is required to remove all the
unwanted parts of the IF spectrum
before the IF signal can be demodulated
to recover the message.
Tuning
Fig.10. Spectra of ‘received’ AM and IF waveforms from Fig.9.
Practical Electronics | January | 2024
It is not the whole story, as we
will see shortly, but the tuning of a
superheterodyne receiver to the desired
station/channel is fundamentally
achieved by a combination of the local
oscillator frequency, which selects
which received frequency is shifted
to the IF, and the bandpass filter after
the IF mixer which removes everything
apart from the wanted signal. This
51
requires a filter with a sharp cutoff
outside the bandwidth of the received
signal; however, because the IF is at
fixed frequency a fixed filter can be
used, which is relatively easy to achieve.
The IF filter was implemented using LC
circuits in the earliest superheterodyne
radios, but later replaced by ceramic
filter components which provide better
accuracy at low cost. As mentioned
above, 455kHz is the traditional IF
frequency for broadcast AM receivers
and many ceramic filters for this (and
other related) IF frequencies were
manufactured. However, some of these
specific components may be harder to
source now as technology has moved
on. (eBay may be your best bet, as is
scavenging old radio equipment.) These
days, filtering (and other processing) of
IF signals can often be achieved using
DSP (digital signal processing).
A bandpass filter is implemented in
the circuit in Fig.8 using two LTspice
second-order behavioural bandpass
filters (U1 and U2). These are configured
as a fourth-order bandpass filter,
centred on the IF frequency of 30kHz,
with a bandwidth which means that
message signal (sidebands) will not
be significantly attenuated. This filter
is for illustration using these example
waveforms and chosen for convenience
of quick set-up in LTspice. It is not
necessarily similar to the requirements
for real radio signals because the IF,
LO and carrier frequencies in the
example are very low for purposes of
displaying the waveforms, and there
are no unwanted signals very close to
the IF frequency in the example.
The waveform of the filtered IF
mixer output (signal filtered) for
the circuit in Fig.8 is shown in Fig.11
with the original message signal for
comparison. We can see that it looks
like an AM signal modulated with the
2kHz sinewave message. The spectrum
of the filtered IF mixer output is shown
in Fig.12 and the frequency response
of the filter is shown in Fig.13 over
the same range as the spectrum. The
frequency response was obtained using
the circuit in Fig.14. Comparison of the
filtered mixer output spectrum with the
unfiltered spectrum in Fig.10 shows
that the signal centred at 190kHz has
been significantly attenuated.
Fig.11. Waveform of filtered IF mixer output from the circuit in Fig.9.
Fig.12. Spectra of filtered IF waveform from the circuit in Fig.9.
Fig.13. Frequency response of the filter (U1 and U2) in Fig.9.
Fig.14. LTspice circuit to obtain the frequency response in Fig.13.
Mixer
Image
filter
RF
amp
IF
filter
IF
amp
Simulation files
Fig.15. Superheterodyne receiver structure.
Most, but not every month, LTSpice
is used to support descriptions and
analysis in Circuit Surgery.
The examples and files are available
for download from the PE website:
https://bit.ly/pe-downloads
52
Practical Electronics | January | 2024
Tuning
Local oscillator
Image frequency
Previously, we discussed using a local oscillator at frequency
fLO = fC + fIF to tune to our required carrier frequency (fC)
and shift the signal to the IF (fIF = fLO – fC). However, the
mixer, with the local oscillator at fLO as one of its inputs,
will also shift a different frequency to f IF , specifically
fIF = fIm – fLO, where fIm is known as the image frequency. We have
fIm = fC + fLO. For example, using the same round numbers
as above, for fC = 1.0MHz and an IF of 400kHz (0.4MHz)
the local oscillator needs to be at 1.4MHz and therefore the
image frequency is at 1.8MHz (1.4 + 0.4 = 1.8MHz). In this
example, if the receiver picks up a signal at 1.8MHz it will
be shifted to the IF along with the wanted signal. Because it
is then at the same frequency, the image cannot be separated
from the wanted signal by filtering after the mixer.
In general, we have to assume that received signals will
be present at the image frequency, so they must be removed
before the mixer. This requires a filter before the mixer,
called the image filter or preselection filter, which may be
tuneable to track with the local oscillator. However, the
requirements for this filter are a lot less severe than if we
tried to filter the required station/channel directly from
the RF signal received from the antenna. In a superhet the
more demanding filtering is done by the fixed frequency IF
filter, as described earlier. The preceding discussion leads
to the structure of a superheterodyne receiver as shown
in Fig.15. There are of course variations on this theme –
for example, there may be another filter before the image
filter to remove all signals outside the band the receiver is
designed to work with. The next stage after the IF amplifier
is detection or demodulation of the IF signal, which we
will look at next month.
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Practical Electronics | January | 2024
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