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System Simulator >
Frequency Domain Analyses >
Multi-Tone Frequency Domain Analysis >
Time Representation of a Bandpass Envelope Multitone RF Signal

Time Representation of a Bandpass Envelope Multitone RF Signal

An important step for calculating IMD products in the time domain is to derive an equivalent envelope time domain representation for a given bandpass RF multi-tone source.

An RF Multi-tone source typically contains a fundamental carrier and at least one additional carrier. The equivalent source voltage V_s(t) of an RF source that has a total of n carriers (including the fundamental carrier) may be expressed as:

where:

f₁ = The fundamental carrier frequency

P₁ = The fundamental carrier available input power
= 0
f_i = The i^th carrier frequency

P_i = The i^th carrier available input power
= The i^th carrier phase (optional)
= In-phase envelope signal

= Quadrature-phase envelope signal

and
,
f_c = f₁

For the multi-tone domain analysis, the carrier frequency should meet the following requirement:

f_c = f₁ + kdf
, ,
where k is a positive or a negative integer.

The quantity is known as the complex envelope of the signal .

Note

Envelope multitone frequency domain analysis results may not be accurate if df is too large. In general, the condition must hold for accurate results. If this condition does not hold, the user must turn on the “Include all harmonics” option. By default, the “Include all harmonics” option is off.

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