Agilent Technologies E1441A user service Modulation, 1 + D ⋅ Am 〈 t〉 ⋅ sin2π ⋅ Fc ⋅ T, Appendix C

Average Value The average value of an ac waveform is the average of the instantaneous values measured over one complete cycle. For sine waves, the average amplitude is zero since the waveform has equal positive and negative half cycles. Since the quantity of interest is the heating value of the signal, the average value of a sine wave is taken to mean the average of the full-wave rectified waveform. The RMS value of a sine wave is equal to 1.11 times the sine wave average amplitude. This relationship does not hold true for other waveshapes.

dBm The decibel (dB) is commonly used to describe RMS voltage or power ratios between two signals. By itself, a decibel value has no particular meaning. Decibels are a ratio or comparison unit and have no absolute meaning without knowledge of a reference or comparison unit. When power comparisons are made to a 1 mW reference level, the letter m is added to give “dBm”. For power ratios such as dBm, it is common to specify the resistance loading the voltage source. Often the system resistance is added to the units by indicating “dBm (50Ω)” for a 50Ω resistance system.

dB = 10 x log10 ( P / Pref )

dBm = 10 x log10 ( P / 0.001 )

where power P = V 2/R

For a 50Ω resistance, 1 mW of power corresponds to 0.224 VRMS.

Use the following conversions to determine dBm levels when connecting 75Ω or 600Ω load resistances.

dBm (75 Ω) = dBm (50 Ω) – 1.75

dBm (600 Ω) = dBm (50 Ω) – 10.79

Modulation

Modulation is the process of combining a high-frequency carrier signal and a low-frequency information signal. How these signals are combined is determined by the specific type of modulation used. The two most common types of modulation are amplitude modulation (AM) and frequency modulation (FM). The information signal that modulates (or varies) the carrier waveform can be of any form — sine wave, square wave, arbitrary wave, or random noise. In general, the carrier signal may also be of any shape, but it is usually a sine wave of constant amplitude and frequency for most communications systems. During modulation, the simple carrier waveform is converted into a complex waveform by the lower-frequency information signal. Generally, the higher-frequency carrier waveform is used to efficiently transmit the complex modulated signal over long distances.

Amplitude Modulation (AM) Amplitude Modulation is a process of producing a waveform whose amplitude varies as a function of the instantaneous amplitude of the modulating information signal. In other words, the information signal creates an amplitude “envelope” around the carrier signal. The Agilent E1441A implements “double sideband transmitted carrier” amplitude modulation similar to a typical AM radio station.

A constant is added to the AM modulating signal so that the sum is always greater than zero (for <100% modulation) as this equation shows:

1 + D ⋅ Am 〈 t〉) ⋅ sin(2π ⋅ Fc ⋅ T

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2

where: "D" is the modulation depth (0 ≤D ≤1.2).

"Am" is the modulating signal with peak amplitude ≤1. "Fc" is the carrier frequency.

An AM waveform with 80% modulation depth. The carrier waveform is a 5 kHz sine wave and the modulating waveform is a 200 Hz sine wave.

158 Agilent E1441A Function Generator Tutorial Appendix C