Bipolar square wave vs unipolar square wave
The amplitude of the third harmonic is 0.21 v. n = the harmonic number, only odd allowedįor example, an ideal square wave with 50% duty-cycle and 0 v to 1 v transition has a first harmonic amplitude of 0.63 v.A n = the amplitude of the n th harmonic.The amplitudes, A n, of the odd harmonics are given by: Equation 2-3 It is only odd harmonics that have values. The amplitudes of all the even harmonics (e.g., 2 GHz, 4 GHz, 6 GHz) are all zero. Luckily, it is possible to calculate the DFT exactly for this special case of an ideal square wave. But what are the amplitudes of each sine wave? The only way to determine this is to perform a DFT on the ideal square wave. We expect to see components at f = 1 GHz, 2 GHz, 3 GHz, and so on. If the ideal square-wave repeat frequency is 1 GHz, the sine-wave frequency values in its spectrum will be multiples of 1 GHz. View the next two pages for the patches for frequency and amplitude modulation.Figure 2-6 Time and frequency domain views of an ideal square wave. Increasing and Decreasing Modulation Frequency In addition, controlling the depth of the second modulator's action will determine how much the first modulator speeds up in this example. One needs to carefully adjust the relative speed of BOTH modulators to get the desired results–usually the second modulator's frequency will be lower than the first one, but that is not absolutely necessary if more audibly random results are desired. That is exactly what the audio example below is doing. For example, if you would like a trill created by a square wave modulator to speed up and slow down, you would route a second modulator into the first modulator’s frequency control input and perhaps use a triangle waveform for the second modulator. Types of sub-audio rate modulation and their effect (click on the modulation types below to play a short example):ĭouble Modulation: Some parameters of a modulating oscillator, such as the frequency or pulse width, can be controlled by a second modulator. In this instance, a regular VCO would be used as the modulator, since most LFO's don't go very far into audio-rate frequency range. An effective synthesis technique may be to sweep the frequency of a modulating oscillator from a sub-audio rate frequency to an audio-rate frequency, causing something like a trill or vibrato to blossom into a panoply of additional frequencies. This can often create additional frequencies, sometimes called sidebands. LFO's may come with a sync option, which when selected causes the waveform to being again at a certain phase with each key on.Īudio-rate modulation, covered on the following pages, occurs when the control oscillator (or noise source) is set above ~20 Hz. Sub-audio rate modulation means the frequency of the modulating oscillator (or noise source) is tuned below 20 Hz, often accomplished by using a Low Frequency Oscillator ( LFO) to save audio rate oscillators for other functions. However, if a square wave was applied, a trill would ensue. Regarding wave shape, if a sine wave was applied to the frequency control input of an oscillator, a smooth up and down vibrato would ensue. Three parameters are key to modulation: rate, depth and wave shape. VCO’s may act as modulators or carriers, depending on how they function in the signal/control paths. source, such as a keyboard to provide, for example, vibrato at different pitches. Often a modulating signal is summed with another c.v. In the case of a carrier oscillator or filter, the initial state is called the center frequency and is set by the offset control of the module. If the modulating wave was a positive unipolar one (a cycle that goes from 0 to +5 volts, for example), it will only be deviated above the initial offset setting. A module will be deviated above and below initial offset state by the undulating voltage of the modulating wave if the modulating source is bipolar, meaning it rises an equal amount above 0 volts as it falls below 0 volts (so for example, a sine wave that peaks at both +5 volts and -5 volts would be considered bipolar). A VCO in the signal path whose frequency is being modulated is known as the carrier. The modulating module providing the oscillating control voltage is known as the modulator. Modulation is the application of AC control voltage from a VCO, LFO (Low Frequency Oscillator) or noise source to other synthesis parameters, such as frequency, filter c.o.f., filter Q amount, amplitude, or pulse width.