SSB modulation, also known as Single Sideband Modulation, is a radio transmission technique that is widely used in modern communication systems. In SSB modulation, only one of the sidebands is transmitted along with the carrier signal, which allows for efficient use of bandwidth. There are two well known SSB modulation method- Frequency Discrimination Method and Phase Discrimination SSB Modulation Method. In this article, we'll take a closer look at SSB modulation using frequency discrimination, what it is and how it works, its benefits and its disadvantages.
At the outset the SSB amplitude modulation circuit diagram using frequency discrimination is shown below.
What is SSB Modulation?
SSB modulation is a method of generation AM signal and is used in AM transmitter. SSB modulation is a technique that involves the suppression of one of the side bands of a double-side band amplitude modulation (DSB-AM) signal. This results in the transmission of only one sideband, along with the carrier signal, which reduces the bandwidth required for transmission.
For example, if the carrier frequency is 200KHz and message signal is 10KHz, the frequency spectrum of standard AM(Amplitude Modulation), DSB-SC AM signal spectrum and SSB signal frequency spectrum.
Standard AM signal frequency spectrum:
SSB AM upper sideband signal frequency spectrum:
SSB AM lower sideband signal frequency spectrum:
As can be seen from the above spectrum, in standard AM modulation, the transmitted AM signal contains carrier signal, upper and lower sideband are transmitted. The transmission bandwidth is of standard AM is equal to twice the message signal bandwidth. In the DSB-SC AM signal transmission, both the sidebands are transmitted but the carrier signal is suppressed, hence it is called DSB-SC(Double Sideband Suppressed Carrier). In the SSB AM signal transmission either the upper or lower sideband of the DSB signal is transmitted. Hence the transmission bandwidth required by SSB signal is equal to the message bandwidth.Thus the difference between standard AM, DSB AM and SSB AM lies in the transmission bandwidth.
Benefits of SSB Modulation
One of the main benefits of SSB modulation is its efficiency in the use of bandwidth. Since only one of the sidebands is transmitted, it reduces the bandwidth required for transmission, allowing for more efficient use of the available spectrum. Additionally, SSB modulation is less susceptible to interference from other signals, making it ideal for long-distance communication.
How SSB Modulation Works
The SSB modulation works by transmitting either upper or lower side band of DSB-SC signal. Let see how the SSB modulation works mathematically. If the message signal is m(t) and the carrier signal is c(t);
\(m(t) = A_m cos(w_m t)\) and \(c(t) = A_c cos(w_c t)\)
we can write the DSB-SC signal as,
\(s_{dsb}(t) = m(t)c(t)\) ------------->(1)
or, \(s_{dsb}(t) = A_m A_c cos(w_m t) cos(w_c t)\)
or. \(s_{dsb}(t) = \frac{A_m A_c}{2} cos[(w_c+w_m)t] + \frac{A_m A_c}{2} cos[(w_c+w_m)t]\) ---->(2)
Let, \(s_{ussb}(t) = \frac{A_m A_c}{2} cos[(w_c+w_m)t] \) ---->(3)
and \(s_{lssb}(t) = \frac{A_m A_c}{2} cos[(w_c-w_m)t] \) ---->(4)
Then we can rewrite, \(s_{dsb}(t) = s_{ussb}(t) + s_{lssb}(t) \) ---->(5)
Expanding (3),
\(s_{ussb}(t) = \frac{A_m A_c}{2} cos[(w_c+w_m)t] \)
or, \(s_{ussb}(t) = \frac{A_m A_c}{2} [cos(w_ct)cos(w_mt)-sin(w_ct)sin(w_mt)] \) --->(6)
Expanding (4),
\(s_{lssb}(t) = \frac{A_m A_c}{2} cos[(w_c-w_m)t] \)
or, \(s_{lssb}(t) = \frac{A_m A_c}{2} [cos(w_ct)cos(w_mt)+sin(w_ct)sin(w_mt)] \) --->(7)
Writing (6) and (7) in compact form,
\(s_{ssb}(t) = \frac{A_m A_c}{2} [cos(w_ct)cos(w_mt) \mp sin(w_ct)sin(w_mt)] \) --->(8)
This equation(8) is the equation for SSB wave where minus sign when used represents upper sideband SSB wave and if positive sign is used the equation represents lower sideband SSB wave. This equation(8) is also the formula for SSB modulation.
We can also write equation(8) as follows,
\(s_{ssb}(t) = \frac{A_m A_c}{2} [cos(w_ct)cos(w_mt) \mp sin(w_ct)sin(w_mt)] \)
\(s_{ssb}(t) = \frac{A_m A_c}{2}cos(w_ct)cos(w_mt) \mp \frac{A_m A_c}{2}sin(w_ct)sin(w_mt) \)
Since \( m(t) = A_m cos(w_m t) \)
and using Hilbert transform of message signal, \( \hat{m(t)} = A_m sin(w_m t) \) --->(9)
we have,
\(s_{ssb}(t) = \frac{A_c}{2}cos(w_ct) m(t)\mp \frac{A_c}{2} \hat{m(t)} sin(w_ct) \) --->(10)
This is the standard equation of SSB modulated wave and it also represents the formula for SSB modulation.
The Hilbert transform a signal is obtained using wideband phase shift filter and the transfer function of such Hilbert transform filter is given by,
\(H(f) = -j sgn(f)\) --->(11)
where sgn(f) is signum function
The SSB modulation method which uses Hilbert transformer filter is called Phase Discrimination Method for generation of SSB modulated wave.
Frequency discrimination SSB modulation circuit
From equation(5) it can be seen that if DSB AM modulator circuit is used to generate DSB-SC AM signal and then apply band pass filter to remove either upper or lower side band of the DSB-SC AM signal we get either lower sideband SSB signal or uppwer sideband SSB signal.
From(5) we have,
\(s_{dsb}(t) = s_{ussb}(t) + s_{lssb}(t) \)
where, \(s_{ussb}(t) = \frac{A_m A_c}{2} cos[(w_c+w_m)t] \)
and, \(s_{lssb}(t) = \frac{A_m A_c}{2} cos[(w_c-w_m)t] \)
This can be generated using DSB modulator.
If we want to generate upper SSB signal then we can build a band pass filter with center frequency \(w_c+w_m\) which will block the lower sideband of the DSB signal. Similarly if we want to generate upper SSB signal then we can build a band pass filter with center frequency \(w_c-w_m\) and remove the upper sideband of DSB signal. Since here we have used filter to remove either one of the sideband of the DSB signal to generate SSB signal this method is called frequency discrimination method of SSB modulation.
The following shows SSB modulation block diagram of frequency discrimination based SSB modulation method.
As shown in the above frequency discrimination of SSB modulation involves the use of a DSB modulator circuit that multiplies the incoming message signal with a carrier signal from local oscillator. The DSB modulator can be transistor based balanced modulator circuit, or balanced ring diode modulator that produces a DSB-AM signal. The DSB modulated signal is then fed into a bandpass filter that removes one of the sidebands. The resulting signal is then amplified and transmitted.
SSB Modulation Frequency Discrimination Video demonstration
See how the SSB modulation circuit works in the following video.
Conclusion
SSB modulation is a powerful technique that offers numerous benefits for radio transmission. By transmitting only one of the sidebands, SSB modulation allows for more efficient use of bandwidth, while also reducing susceptibility to interference. Understanding how SSB modulation works is essential for anyone working in the field of radio communication.
