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salim943 authored Aug 23, 2024
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30 changes: 10 additions & 20 deletions experiment/theory.md
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<link href="https://cdn.jsdelivr.net/npm/tailwindcss@2.2.19/dist/tailwind.min.css" rel="stylesheet">
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<p>
Similar to amplitude-modulated (AM) signals, double sideband full carrier (DSB-FC) signals include both the upper and lower sidebands along with the carrier signal. <br>In contrast, double sideband suppressed carrier (DSB-SC) modulation transmits only the sidebands of the modulated signal, omitting the carrier signal itself. For single sideband suppressed carrier (SSB-SC) modulation, the original message signal can be reconstructed using only one sideband—either the upper or the lower. In this case, only the selected sideband (upper or lower) is transmitted. Hence transmission bandwidth can be cut by half if one sideband is entirely suppressed. This leads to single sideband modulation (SSB). In SSB modulation bandwidth saving is accompanied by a considerable increase in equipment complexity.
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</a>
</li>
<li>
<a href="./theory/DSBSC_Demod.html">
<div class="flex">
<span class="text-black mr-4">2.</span>
<p class="hover:text-[#3e6389] hover:underline">
DSB-SC Demodulation
</p>
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</a>
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<li>
<a href="./theory/SSBSC.html">
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</a>
</li>
<li>
<a href="./theory/SSBSC_Demod.html">
<div class="flex">
<span class="text-black mr-4">4.</span>
<p class="hover:text-[#3e6389] hover:underline">
SSB-SC Demodulation
</p>
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111 changes: 110 additions & 1 deletion experiment/theory/DSBSC.html
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<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<script src="https://cdn.tailwindcss.com"></script>
<script type="text/javascript" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>
<title>Virtual Labs</title>
<link rel="stylesheet" href="../css/vlabs-style.css" />
<link rel="shortcut icon" href="../images/favicon.ico" />
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>
DSB-SC Modulation
</h2>
<h3 class="text-[24px] font-semibold text-black">Block Diagram</h3>
<h3 class="text-[24px] font-semibold text-black">Theory</h3>
<p>
Double Sideband Suppressed Carrier (DSB-SC) modulation is a type of amplitude modulation where only the sidebands
are transmitted, and the carrier signal is suppressed. This method is more power-efficient compared to standard
amplitude modulation (AM), as it eliminates the carrier, which does not carry useful information.
</p>

<h2>Mathematical Representation</h2>
<p>The DSB-SC modulated signal \( S(t) \) can be expressed as:</p>
<p>
\( S(t) = A_c m(t) \cos(2\pi f_c t) \)
</p>
<p>Where:</p>
<ul>
<li>\( A_c \) is the amplitude of the carrier signal.</li>
<li>\( m(t) \) is the baseband (modulating) signal.</li>
<li>\( f_c \) is the frequency of the carrier signal.</li>
</ul>
<p>
In DSB-SC modulation, the carrier signal \( \cos(2\pi f_c t) \) is multiplied by the modulating signal \( m(t) \),
resulting in the modulated signal \( S(t) \). The key characteristic of DSB-SC is that the carrier \( A_c \cos(2\pi f_c t) \)
is not transmitted. Instead, only the sidebands generated by the multiplication of \( m(t) \) and \( \cos(2\pi f_c t) \)
are transmitted.
</p>
<br>

<h3 class="text-[24px] font-semibold text-black">Block Diagram</h3>

<div class="flex justify-center gap-20 bg-blue-50">
<img
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edge still further until the amplitude of this sine wave just starts
to reduce. Record the filter pass band edge as fB. <br /><br />
</p>


<br>
<hr>
<br>
<h2
class="text-center pt-6 border-b pb-2 mb-2 text-[#2C99CE] text-[32px]"
>
DSB-SC Demodulation
</h2>
<h3 class="text-[24px] font-semibold text-black">
DSBSC Demodulation :
</h3>
<p>
Recovering the message signal from the demodulated signal is
performed coherently. That is, the demodulated signal is multiplied
by a high-frequency sinusoid in perfect synchronization (in phase
and frequency) with the incoming carrier.
<br />
<br />
This requirement poses a challenge on the design of the demodulator
circuit, as it would then require a part for carrier-recovery.
Failing to accomplish perfect synchronization will result in phase
mismatch or frequency mismatch, leading to some form of distortion
in the recovered signal.
<br />
<br />
Multiplying the modulated signal with a local carrier will produce a
baseband signal as well as a signal modulated at double the carrier
frequency. Therefore, a LPF is needed at the far end of the
demodulator to recover the baseband signal .
</p>
<h3 class="text-[24px] font-semibold text-black">
DSBSC Demodulation Block Diagram
</h3>

<div class="flex justify-center gap-20">
<img
src="../images/theory/dsbsc_demod1.png"
alt="dsbsc_image1"
class="h-[280px]"
/>
</div>
<p class="mb-4 text-center font-semibold text-black">
Fig. DSB-SC Demodulation Block Diagram
</p>
<!-- -->
<h3 class="text-[24px] font-semibold text-black">Procedures :</h3>
<p class="pl-3">
<span class="font-semibold">1. </span> Use the same carrier signal
used in DSBSC modulation, multiplier and a Tunable LPF to demodulate
the DSBSC generated during DSBSC modulation.
</p>
<div class="flex justify-center">
<img
src="../images/theory/dsbsc_demod2.png"
alt="dsbsc_image2"
class="h-[440px]"
/>
</div>
<p class="mb-4 text-center font-semibold text-black">
Fig. The TIMS Model of The Block Diagram of DSB-SC Demodulation
</p>
<p class="ml-3">
<span class="font-semibold">2. </span> Switch the Scope Selector to
CH1-A and CH2-B.
<br />
<span class="font-semibold">3. </span>Observe the signal in time and
frequency domains before and after the LPF simultaneously.
<br />
<span class="font-semibold">4. </span>Vary the cutoff frequency of
the LPF, and find the range of acceptable values for best recovery
of the message.
<br />
<span class="font-semibold">5. </span> Plot, in time, the best
recovered signal you can obtain in your lab sheets.
<br />
<span class="font-semibold">6. </span> Increase the cutoff frequency
of the LPF beyond the range of good recovery.
</p>

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<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<script src="https://cdn.tailwindcss.com"></script>
<script type="text/javascript" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>
<title>Virtual Labs</title>
<link rel="stylesheet" href="../css/vlabs-style.css" />
<link rel="shortcut icon" href="../images/favicon.ico" />
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>
SSB-SC Modulation
</h2>

<h3 class="text-[24px] font-semibold text-black">Theory</h3>
<p>The SSB-SC modulated signal \( S(t) \) can be expressed as:</p>
<p>
\( S(t) = \frac{A_c}{2} \left[ m(t) \cos(2\pi f_c t) \pm \hat{m}(t) \sin(2\pi f_c t) \right] \)
</p>
<p>Where:</p>
<ul>
<li>\( A_c \) is the amplitude of the carrier signal.</li>
<li>\( m(t) \) is the baseband (modulating) signal.</li>
<li>\( f_c \) is the frequency of the carrier signal.</li>
<li>\( \hat{m}(t) \) is the Hilbert transform of the modulating signal \( m(t) \).</li>
</ul>
<p>
In SSB-SC modulation, either the upper sideband (USB) or the lower sideband (LSB) is transmitted by choosing the corresponding sign (plus or minus) in the equation.
The carrier \( A_c \cos(2\pi f_c t) \) is suppressed, and only one sideband is transmitted. This reduces the bandwidth required for transmission to half that of DSB-SC.
</p>
<br>

<h3 class="text-[24px] font-semibold text-black">Block Diagram</h3>

<div class="flex justify-center">
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>
</div>


<br>
<hr>
<br>
<h2
class="text-center pt-6 border-b pb-2 mb-2 text-[#2C99CE] text-[32px]"
>
SSB-SC Demodulation
</h2>
<h3 class="text-[24px] font-semibold text-black">Block Diagram</h3>

<div class="flex justify-center">
<img
src="../images/theory/ssbsc_demod1.png"
alt="ssbsc_demod1"
class="h-[280px]"
/>
</div>
<p class="mb-4 text-center font-semibold text-black">Figure 1</p>
<h3 class="text-[24px] font-semibold text-black">Procedures :</h3>
<p class="ml-3">
<span class="font-semibold">1. </span> This is an asynchronous
demodulation process. Here frequency of the VCO is adjusted with the
frequency counter.

<br />
<span class="font-semibold">2. </span>It is quite easy to make small
frequency adjustments (fractions of a Hertz) by connecting a small
negative DC voltage into the VCO Vin input, and tuning with the GAIN
control.

<br />
<span class="font-semibold">3. </span>Here, VCO facilitates fine
tuning. Even if the frequency difference between the original
carrier frequency (e.g., 100 KHz) and the frequency of the VCO
differs by 10 Hz, then demodulated signal / speech will be quite
intelligible

<br />
<span class="font-semibold">4. </span>A recommended method of
showing the small frequency difference between the VCO and the 100
kHz reference is to display each on separate oscilloscope traces -
the speed of drift between the two gives an immediate and easily
recognised indication of the frequency difference.

<br />
<span class="font-semibold">5. </span>Connect an SSB signal, derived
from speech, to the input ‘X’ of the multiplier as shown in the
figure 1. Tune the VCO slowly around the 100 kHz region, and listen.
Report results. <br />
<br />
</p>


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