Time Domain Representation of a Multitone RF Source

The nonlinear functional component part of a nonlinear behavioral element (See Figure 2 in the topic The Equivalent Model for Nonlinear Behavioral Components ) is modeled in the time domain. 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.

Complex Envelope of an RF Source

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

= The complex envelope of the signal S(t)

= In-phase envelope signal

= Quadrature-phase envelope signal

Where:

f_i = The i^th carrier frequency

f₁ = f_c = Fundamental carrier frequency

q₁ = 0

q_i = The i^th carrier phase

P_i = The i^th carrier available input power

P₁ = Fundamental carrier available input power

Nonlinear Output Voltage

The nonlinear output voltage is calculated in the time domain as:

Where:

The source resistance R_in and the load resistance R_out default to 50W, but they can be individually specified for each input and output, respectively.

Constraints on the Carrier Frequency

The accuracy of the envelope multi-tone analysis puts constraints on the minimum spacing between carrier frequencies:

, , i,j = 1,2...,n

k = positive or negative integer.

Envelope multitone frequency domain analysis results may lose accuracy when Df is too large. In general, the condition Df << f₁ must hold for accurate results.