# Tag Archive for Amplitude modulation

Hi folks! This week we have introduced the first in a series of analog ICs – the AD633 multiplier IC. This is a functionally complete, four-quadrant, analog multiplier. Four quadrant means that both operands that are multiplied can take any polarity i.e. +/- and hence multiplication can happen across 4 quadrants. It includes high impedance, differential X and Y inputs, and a high impedance summing input (Z). Thus this multiplier basically does a MAC operation (Multiply and Accumulate). The AD633 is well suited for such applications as modulation and demodulation, automatic gain control, power measurement, voltage-controlled amplifiers, and frequency doublers. The input range of operating voltages for this IC is from +15 V to -15 V. So while designing circuits with AD633 keep in mind that the inputs do not exceed this limit. Typically this IC provides a bandwidth of 1  MHz. [1]

Let’s check out a few applications using AD633 on DoCircuits. First up, given below is an amplitude modulator circuit. ( Click on the circuit to load it on DoCircuits)

The carrier and modulation inputs to the AD633 are multiplied to produce a double sideband signal. The carrier signal is fed forward to the Z input of the AD633 where it is summed with the double sideband signal to produce a double sideband with the carrier output. Here is how the AM signal generated looks like:

Another very simple application using the AD633 is the voltage controlled low pass filter. The cutoff frequency is modulated by EC, the control input. ( Click on the circuit to load it on DoCircuits )

Using the above circuit we get the following output:

Low Pass Filter using AD633 Output

Now to show how you can control this low-pass filter we can sweep the control voltage (Vdc) from 0.01 V to 0.02 V (this is done by selecting Frequency Domain Analysis and enabling the sweep settings. Then vary the Vdc values as given) and plot the frequency response as shown:

Low Pass Filter Using AD633 output sweep

So where can we find such a low-pass filter? In some popular electronic music styles, “filter sweeps” have become a common effect. These sweeps are created by varying the cutoff frequency of the VCF (sometimes very slowly) [2]

References:

2. http://en.wikipedia.org/wiki/Voltage-controlled_filter

# System Modeling using DoCircuits

The other day my friend and I were supposed to design an AM modulator – an ideal one – that can work out for practically any carrier and message (modulating signal) signal. One way to do it would be to design an AM circuit the traditional way using BJT et al. Well what’s wrong with it? One is the accuracy. We won’t get an accurate representation of the AM wave. It will depend on so many other things like the BJT biasing, its properties etc. And also we would have had to take the trouble to design the circuit! (Ouch!) So we decided to model the circuit using ideal components like the multiplier (after all the AM operation itself is a function in multiplication).

So anyone can recall the equation for an AM operation? We did our research and ended up with this:

y(t) = [1 + m(t)].c(t)

= A[1 + Mcos(2πfm t]sin(2πfc t)

M= modulation index

fm= modulation frequency

fc= carrier frequency

A= amplitude of carrier

This equation is used for a sine carrier and sine modulating wave. Let’s see how by modelling this equation and making a few changes we can model an AM waveform for a sine wave modulating signal and square carrier signal. If I were to directly implement the above equation using ideal components it will look like this: ( Circuit Here )

The carrier is supposed to be a square wave of amplitude 6 V and frequency 10 kHz. From this frequency the square wave TL and TH are set as 0.05 ms. Since for the square wave source U value is a peak-to-peak amplitude, we add an offset of -6 V to get the amplitude from +6 to -6. From the equation it is known that an offset of A should be added to the modulating wave. “A” here is the amplitude of the carrier wave. Thus the sine wave modulating wave is given an offset of 6 V. The amplitude of the sine wave is determined by the modulation index. Say I want a modulation index of 50%.  Thus the amplitude of the sine modulating wave is set as 3 V with a frequency of 1 kHz. These two signals are multiplied with the help of a multiplier.

There you go, we have modelled an AM system from the equation for AM. Whether we are successful is yet to be seen. Simulating the above circuit gives the following output:

We seem to have succeeded but let’s verify if the modulation index matches if calculated from the plot.

M= (54-18)/(54+18)  – modulation index is given by (Vmax-Vmin)/(Vmax+Vmin)

After calculation the modulation index is found to be 36/72 = 0.5 or 50%. Thus our method is pretty accurate.

This example is just one of many types of systems that can be modelled in DoCircuits. Of course you can extend the above method to all the different types of signals like sine, triangular, square etc. both as carrier and modulating wave. But what is the idea behind it all? It all started by getting the equation for a system and trying to implement it by modelling it in DoCircuits. Basic operations like addition, subtraction, division and multiplication are available in the ideal components panel and can be modelled very easy at present and further operations will be added in the future.

You must have seen the radio that your grandfather loved listening to as you grew up.  I bet you loved turning the tuner knobs either way when no one was around!

You always wanted to know what the letters “AM” and “FM” meant. Today lets try to decode one of them. But before that, lets try and understand – What is modulation? Modulation is the process of changing a characteristic of a carrier wave with respect to a modulating wave. This modulating wave is otherwise known as the message signal which has the information to be transmitted. For example in amplitude modulation (AM), the amplitude of the carrier signal is varied in accordance with the modulating signal.

Amplitude modulation, more popularly known in its abbreviated form as “AM”, is a method of communication used mostly in the form of radio waves.  Amplitude modulation was originally engineered for use with the electric telephone (modern-day telephone) to add audio to a receiver connected to a telephone transmitter. In 1906 conducted an audio exhibition using amplitude modulation to broadcast audio signals using radio waves. From the exhibition in 1906 to modern day radio broadcasting, AM is still being used, referred to as the “AM Band”.

Another way is FM (Frequency Modulation). While FM offers greater clarity for audio, and the higher frequencies that FM use offer a wider bandwidth, allowing for more information to be transmitted, one application where FM and digital are not suitable are Aviation communication, which to this day still use AM analogue. This is because weaker signals can be heard over stronger, closer ones with AM, allowing for emergency transmissions to have more chance of being heard over other traffic. Also, AM uses a narrower bandwidth than FM, allowing more users in a smaller space. This is important for the lower frequencies of Radio, where space is at a premium.

The next question is why do we have to modulate any signal? The alternative to modulating a wave and transmitting it is to send the wave as it is un-modulated. The first obstacle in doing that is the receiving the information. For efficient radiation and reception the transmitting and receiving antennas would have to have lengths comparable to a quarter-wavelength of the frequency used. In other words the shorter the wavelength (higher the frequency) the shorter the antenna need be. As a result of modulation, the low frequency message signal is ‘carried’ by a wave with a higher frequency.

The transmitted messages in AM radio are mainly music and voice in the audible range of 20 – 20 kHz. Due to this all the signals from all the AM stations will be mixed up in a very small band of frequencies. It would be difficult to separate the required message signals at the receiver unless they are converted to different frequencies of the electromagnetic spectrum. At the receiver a tuned circuit will be present to extract the required frequency for demodulation.

Let us see a circuit in which the given carrier is modulated depending on the modulating signal.

The BJT must be biased properly to get a correct output. The carrier is connected to the base and this is amplified by the BJT and flows in the collector, but again the current is restricted by the opposing flow from the modulating wave connected to the emitter. As a result the output amplitude is varied according to the opposing modulating voltage.

One thing should be maintained in the AM circuit. That is that the message signal voltage (Vm) should be less than the carrier voltage (Vc). This relationship is known as the modulation index (Vm/Vc) and it should be between 0 and 1. When it is more than 1, or if the Vm is more than Vc, then distortion occurs. Let’s see the output of the above circuit – the modulated wave. Run the circuit by clicking here.

Verify the frequency of the signal to be equal to the carrier frequency. Also note that the envelope of the modulating wave varies with reference to the carrier wave. So the amplitude of the modulating wave should be less than the carrier signal amplitude else the wave distorts. If the wave is distorted then a portion of the trough in the modulating wave will be clipped. As a result information is lost. You can see it practically by varying the amplitudes in our simulation and see the effects.

The expression for the modulation index is given as m= Vm/Vc = (Vmax – Vmin)/(Vmax + Vmin). Vm = (Vmax – Vmin)/2 and Vc = (Vmax + Vmin)/2. Refer the diagram given below.

The frequency spectrum would give the frequency components in the AM modulated wave. The frequency spectrum cannot be plotted in DoCircuits like the frequency response. But you can reads more information about it from here:

Some useful video links are this and this.