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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