Analog Pulse Modulation

This chapter is dedicated to analog pulse modulation characterized by the use of an analog reference input to the pulse modulator. It is attempted to devise modulation strategies that will lead to the optimal PMA performance. This is carried out by a fundamental review and comparison of known pulse modulation methods, followed by investigations of new enhanced pulse modulation methods with improved characteristics. The analysis is based on the derivation of Double Fourier Series (DFS) expressions for all considered methods, and the introduction for a spectral analysis tool – the Harmonic Envelope Surface (HES) – based on the analytical DFS expressions. The HES offers detailed insight in the (for PMAs) interesting aspects and the tool proves indispensable of a coherent analysis and comparison of extensive set of pulse modulation methods that are investigated throughout this chapter. A new multi-level modulation method – Phase Shifted Carrier Pulse Width

Modulation (PSCPWM) [Ni97b] – is introduced and subjected to a detailed investigation. A suite of PSCPWM methods are defined each with distinct characteristics, and it will appear that the principle provides optimal pulse modulation for PMAs from a theoretical point of view.

Fundamental pulse modulation methods

Pulse modulation systems represent a message-bearing signal by a train of pulses. The four

basic pulse modulation techniques are [Bl53] Pulse Amplitude Modulation (PAM), Pulse

Width Modulation (PWM), Pulse Position modulation (PPM) and Pulse Density

  1. PAM:Pulse-amplitude modulation(PAM), is a form of signalmodulationwhere the message information is encoded in theamplitudeof a series of signalpulses. It is an analogpulse modulationscheme in which theamplitudesof a train of carrierpulsesare varied according to the sample value of the message signal.
  2. PWM:Pulse Width Modulation, orPWM, is a technique for getting analog results with digitalmeans. Digital control is used to create a square wave, a signal switched between on and off.
  3. Pulse-position modulation(PPM) is a form of signalmodulationin which M message bits are encoded by transmitting a singlepulsein one of possible time-shifts. This is repeated every T seconds, such that the transmitted bit rate is bits per second.
  4. Pulse-density modulation, or PDM, is a form ofmodulationused to represent an analog signal with digital data. In a PDM signal, specific amplitude values are not encoded intopulsesof different size as they would be inpulse-codemodulation(PCM).

Modulation (PDM). Fig. 2.1 illustrates these four fundamental principles of analog pulsemodulation.

Pulse Amplitude Modulation (PAM) is based on a conversion the signal into aseries of amplitude-modulated pulses as illustrated in Fig. 2.1. The bandwidth requirementsare given by the Nyquist sampling theorem, so the modulated signal can be uniquelyrepresented by uniformly spaced samples of the signal at a rate higher or equal to two timesthe signal bandwidth. An attractive feature of PAM is this low bandwidth requirementresulting in a minimal carrier frequency, which would minimize the power dissipation in aswitching power amplification stage. Unfortunately, PAM is limited by the requirementsfor pulse amplitude accuracy. It turns out to be problematic to realize a high efficiencypower output stage that can synthesize the pulses with accurately defined amplitude. If onlya few discrete amplitude levels are required, as it is the case with the other three pulsemodulation methods, the task of power amplification of the pulses is much simpler.

Pulse Width Modulation (PWM) is dramatically different form PAM in that it performssampling in time whereas PAM provides sampling in amplitude. Consequently, theinformation is coded into the pulse time position within each switching interval. PWMonly requires synthesis of a few discrete output levels, which is easily realized bytopologically simple high efficiency switching power stages. On the other hand, thebandwidth requirements for PWM are typically close to an order of magnitude higher thanPAM. This penalty is well paid given the simplifications in the switching power stage /power supply.

Pulse Position Modulation (PPM) differs from PWM in that the value of eachinstantaneous sample of a modulating wave is caused to vary the position in time of apulse, relative to its non-modulated time of occurrence. Each pulse has identical shapeindependent of the modulation depth. This is an attractive feature, since a uniform pulse is

simple to reproduce with a simple switching power stage. On the other hand, a limitation of

PPM is the requirements for pulse amplitude level if reasonable powers are required. Thepower supply level of the switching power stage will have to be much higher than therequired load voltage. This leads to sub-optimal performance on several parameters asefficiency, complexity and audio performance.

Pulse Density Modulation is based on a unity pulse width, height and a constant time ofoccurrence for the pulses within the switching period. The modulated parameter is thepresence of the pulse. For each sample interval it is determined if the pulse should bepresent or not, hence the designation density modulation. It is appealing to have a unitypulse since this is easier to realize by a switching power stage. Another advantage is thesimplicity of modulator implementation. However, PDM requires excess bandwidthgenerally beyond what is required by e.g. PWM.

A qualitative comparison of the four fundamental methods is shown in Table 2.1. Only

PDM and PWM are considered relevant, i.e. potential candidates to reach the targetObjectives.