# Two-Box-Model of a nonlinear amplifier

A nonlinearity with memory can be modelled by a two-box-model, which consists of a filter and a memoryless nonlinearity. I am referring to chapter 5.3.2 of the book "Simulation of Communication Systems" by M.C.Jeruchim et. al. here's a link to Google books

I am given the AM-AM- and the AM-PM-characteristic of an amplifier. I want to model the behavior of the amplifier to a two-tone input signal. To do so, I want to set up a two-box-model. The memoryless nonlinearity should be described by the given characteristics.

• But what does a filter before the memoryless nonlinearity do?
• What does an ARMA filter do?
• Can an ARMA filter be used to filter an analog signal (sine-waves) ?
• Hi Luk, you brought up the term "two-box model", so I think it'd be only fair to us if you referred to the source where you've got that from. I'm not asking for this because I want to be nitpicky - it's just that I actually already answered a question you asked by pointing out a sentence in the paper you forgot to cite in the original version of your question, and had you specified your sources right from the start, you could have saved me a lot of work. Jan 3 '17 at 19:02
• To my understanding, "two-box models" don't always consist of a filter and a nonlinearity, so your question is literature-specific, so you must at least specify which literature you're referring to. Jan 3 '17 at 19:03
• you're right, I didn't think about it.
– user25356
Jan 4 '17 at 8:43
• ARMA filters operate on discrete-time data. I've added some information to my answer. Jan 4 '17 at 10:02

An ARMA (or IIR) filter is a discrete-time (linear time-invariant) filter whose response $y[n]$ to an input sequence $x[n]$ is computed as follows:
$$y[n]=\sum_{m=0}^Mb_mx[n-m]+\sum_{l=1}^Na_ly[n-l]\tag{1}$$
where $b_m$ and $a_l$ are the filter coefficients, which are chosen such that a certain desired filter characteristic (e.g., low pass, high pass, etc.) is achieved.
• thx, Matt! I am given a superposition of 2 sine-waves. I think this signal can be considered discrete as I am given the values of the signal at different time steps ( so I have a vector). I have a vector of the output signal as well. I think the main goal of a filter before my nonlinearity is to filter out the 3rd-degree intermodulation products of my output spectrum. At least it would be great, if this was possible! In equation (1), m and l are just the indices of the vector entries, right? And now my task is to determine $a_l$ and $b_m$ - is this where least squares is used?