# P1dB

P1dB (input-referred) is the input power where the output power is compressed 1dB from the ideal output power. It may be considered as an acceptable operating point in compression.

			
% model for P1dB 1dB compression point

clear; clc;
close all;

Vin = 1 : 1 : 50; % input power in dB
A = 40; % cliipping level

Vo_ideal = Vin; % ideal output

plot(Vin, Vo_ideal, 'b');
hold on;

Vo = f_rapp(A, Vin, 2); % rapp model

plot(Vin, Vo, 'r');
legend('ideal','Vo');
xlabel('Vin(dB)');
ylabel('Vo(dB)');
grid on;

% find P1dB;
Vcomp = Vo_ideal - Vo; % find delta
[N,bin]=histc(1,Vcomp); % find closest index to 1dB
P1dB = Vin(bin); % find input power when delta is 1dB

fprintf('P1dB = %f\n', P1dB);



To model power amplifier compression, the Rapp SSPA (solid state power amp) model1 is used below. In this model, $$\ V_{out} = {V_{in} \over {(1 + {({V_{in} \over V_{sat}})^{2*p}})^{1 \over {2p}}}}$$ \ \begin{align} V_{out}& = output \ level \\ V_{in}& = input \ level \\ V_{sat}& = saturation \ level \\ p& = smoothness \ parameter \\ \end{align}

			
function [ Vo ] = f_rapp( A, Vin, p )
% f_rapp Rapp model for power amplifier
%
% Developed for solid-state power amplifiers.
% Produces a smooth transition for the envelope characteristic
% as the input amplitude approaches saturation.
% Where Vsat is the saturation voltage of the power amplifier and
% P is the smoothness factor.

Vsat = A/sqrt(2);
Vo = Vin./(1+(abs(Vin)/Vsat).^(2*p)).^(1/(2*p)); % rapp power amp model

end P1dB = 19.000000



## References:

1. Ashraf A. Eltholth, Adel R. Mekhail, A. Elshirbini, M. I. Dessouki† and A. I. Abdelfattah
Modeling the Effect of Clipping and Power Amplifier Non-Linearities on OFDM Systems
2. David Falconer, Carleton University Tom Kolze, Broadcom, Yigal Leiba, Breezecom, John Liebetreu, Sicom
Proposed System Impairment Models
3. R&S®ZVA network analyzer basics part 5: Non-linear amplifier tests
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