Modulation advances have fueled more efficient use of bandwidth, although conventional modulation formats still require allowance for upper and lower sidebands around the carrier frequency. Ultra narrowband modulation, however, is an efficient form of transmitting information without using sidebands. The modulation format, which is also known as very minimum sideband keying (VMSK) or minimum sideband (MSB) modulation, has been in development since 1985. Although stalled since that time due to the lack of practical filters, the modulation method is now available to system developers through the use of filtering techniques with zero group delay.

A review of more conventional modulation formats, such as frequency modulation (FM) and phase modulation (PM), may help when attempting to understand MSB modulation. For example, in conventional modulation formats, changes in frequency and phase occur gradually (right-hand side of Fig. 1), compared to the abrupt changes in frequency and phase of MSB modulation (left-hand side of Fig. 1). MSB digital modulation utilizes a coded baseband with abrupt edges; that is, the rise/fall times are as abrupt or near zero as possible. Some resistive-capactive (RC) rise time is inevitable, due to slew rates in integrated circuits (ICs) and other parts of the transmitter/receiver circuitry. In practice, these changes occur during one cycle of the intermediate frequency (IF).

For example, the frequency resulting from a modulating input signal is F = F_carrier + Δf, where the modulation frequency, Δf, can be calculated from the basic relationship of ωt = φ = 2πft. The modulation frequency can also be rewritten in derivative form as Δf = Δφ/2πt. The rise/fall time, t, is fixed by the circuit parameters. During rise/fall times for abrupt phase modulation, there is a large Δφ/Δt which causes large Δf (almost infinite) for a very short duration (about 1 cycle at RF). At all other times, Δφ is zero and the frequency is constant at F = F_carrier. A phase detector using F_carrier as a phase reference will detect the phase changes as positive and negative voltages, but will ignore large Δf. In this case, consider Δφ as being zero for most of the bit (information) period.

The situation is different for the waveform in the right-hand side of Fig. 1. In that case, Δφ has a finite value and lasts for the entire period of the phase change. There is a definite change in frequency for the phase change period. Armstrong² used this concept to produce FM from PM in 1936. If Δφ/Δt is caused by a sine wave, the resulting FM is a cosine wave, since FM is the derivative of PM.

The abrupt phase change and resulting frequency change in the left-hand side of Fig. 1 was noted by Professor Howe in 1939.¹ The observation was not applied since digital-modulation techniques were not in use at that time, and the filters needed to take advantage of the abrupt phase changes were not available.

Any bandpass filter used at the transmitter for ultra narrowband (MSB) modulation must exhibit zero group delay to pass the instantaneous phase changes, though it may lack the bandwidth required to pass instantaneous changes in frequency. To all intents and purposes, there is no measurable frequency change, but there is a phase change in the carrier that is maintained constant between the rise and fall times. A conventional, or Nyquist filter, has group delay and rise time. This causes the phase modulation to spread out over time, and the result is FM (right-hand side of Fig. 1).

According to accepted practice using PM to generate FM (the Armstrong method), a carrier and upper and lower sidebands are required (Fig. 2).² The vectors for the upper and lower sidebands counter-rotate in phase, reaching a maximum in either direction when they are at the same phase. The upper sideband (USB) is a signal higher in frequency than the carrier by an amount equal to the modulation frequency. The lower sideband (LSB) is lower in frequency than the carrier by the same amount. This gives rise to Bessel products, which are necessary to cause the vector V4 to shift in phase. There are three or more different frequencies involved to produce the phase shift, φ.³

The equivalents of the USB and LSB are seen as vectors V2 and V3 when using abrupt phase modulation. They must maintain the phase shift, φ, at a constant angle, hence they cannot rotate, but can only reverse. If they do not rotate, they are not at different frequencies, but at the same frequency as the carrier V1.

Abrupt phase-angle modulation does not require any frequencies other than the carrier. There are no Bessel products or other frequencies required to produce the phase shift. This is obvious from the mathematics. If the modulation frequency, Δf is equal to Δφ/2πt, and the change in the phase shift, Δφ, is zero, then Δf is zero. The level of the J_n Bessel products, as referenced from a Bessel function table, is determined by β = Δφ. If β = 0, there are no Bessel products other than the J₀ product.³

When using a coded baseband to produce the rectangular waveform in the left-hand side of Fig. 1, and using 90-deg. abrupt phase modulation, the spectrum of Fig. 3 would result. Non-return-to-zero (NRZ) information from a CMOS driver is used to avoid having an unfamiliar baseband code for this example (with a data rate of 270 kb/s using random data). The dome-shaped base of the spectrum is the sum of the Fourier frequencies associated with random NRZ data. Although the Fourier products are amplitude products only, they do appear using this modulation method. They do not cause any phase shift and can be reduced by zero-group-delay filtering.