-------------------------------------------------------------------------------
-- Copyright (c) 2003 Mentor Graphics Corporation
--
-- This model is a component of the Mentor Graphics VHDL-AMS educational open 
-- source model library, and is covered by this license agreement. This model,
-- including any updates, modifications, revisions, copies, and documentation 
-- are copyrighted works of Mentor Graphics. USE OF THIS MODEL INDICATES YOUR 
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-- IN THIS LICENSE AGREEMENT.  Mentor Graphics grants you a non-exclusive 
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-- notice that this model has been modified and the date of modification; and 
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-- conspicuous notice that this model is available from Mentor Graphics in its
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--
-- THIS MODEL IS LICENSED TO YOU "AS IS" AND WITH NO WARRANTIES, EXPRESS OR 
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-------------------------------------------------------------------------------
-- File       : e_LPF_2nd.vhd
-- Author     : Mentor Graphics
-- Created    : 2002/05/20
-- Last update: 2003-05-20
-------------------------------------------------------------------------------
-- Description: 2nd order Lowpass Filter with electrical connections.
-------------------------------------------------------------------------------
-- Revisions  :
-- Date        Version     Author              Description
-- 2001/11/27  1.0         Mentor Graphics     Created
-- 2003/04/15  1.1         Mentor Graphics     Added z-domain architecture
-------------------------------------------------------------------------------
library IEEE;
use IEEE.MATH_REAL.all;
library IEEE;
use IEEE.electrical_systems.all;

entity e_LPF_2nd is
  generic ( K    : real := 1.0;    -- Filter Gain
            Fp   : real := 100.0;  -- Double Pole Frequency [Hz]
            Q    : real := 0.707;  -- Quality factor
            Fsmp : real := 10.0e3  -- For Z-dmn only: Sample frequency (in Hz)
            );
  port ( terminal input  : electrical;
         terminal output : electrical
         );
end entity e_LPF_2nd;
-------------------------------------------------------------------------------
-- Transfer Function:
--
--                      wp^2
-- Vo(s) = K * --------------------- Vin(s)
--             wp^2 + (wp/Q)*s + S^2
-------------------------------------------------------------------------------

-- S Domain Implementation
architecture s_dmn of e_LPF_2nd is
  quantity vin across input;
  quantity vout across iout through output;
  constant wp  : real        := math_2_pi*Fp;       -- Frequency in Radians
  constant num : real_vector := (wp*wp, 0.0, 0.0);  -- Numerator array
  constant den : real_vector := (wp*wp, wp/Q, 1.0); -- Denominator array
begin
  vout == K * vin'ltf(num, den);        -- Laplace Transform of input
end architecture s_dmn;

-- Z Domain Implementation (via bilinear transform, no pre-warping)
architecture z_dmn of e_LPF_2nd is
  quantity vin across input;
  quantity vout across iout through output;
  constant T   : real := 1.0/Fsmp;          -- Sample period
  constant wp  : real := math_2_pi*Fp;      -- Frequency in Radians 
  constant n0  : real := Q*T**3*wp**2;      -- num z-0 
  constant n1  : real := 3.0*Q*T**3*wp**2;  -- num z-1 
  constant n2  : real := 3.0*Q*T**3*wp**2;  -- num z-2 
  constant n3  : real := Q*T**3*wp**2;      -- num z-3 
  constant d0  : real := 4.0*Q*T + 2.0*T**2*wp + Q*T**3*wp**2;       -- den z-0
  constant d1  : real := -4.0*Q*T + 2.0*T**2*wp + 3.0*Q*T**3*wp**2;  -- den z-1
  constant d2  : real := -4.0*Q*T - 2.0*T**2*wp + 3.0*Q*T**3*wp**2;  -- den z-2
  constant d3  : real := 4.0*Q*T - 2.0*T**2*wp + Q*T**3*wp**2;       -- den z-3
  constant num : real_vector := (n0, n1, n2, n3);  -- Numerator array
  constant den : real_vector := (d0, d1, d2, d3);  -- Denominator array
begin
  vout == K * vin'ztf(num, den, T);     -- Z-domain transfer function
end architecture z_dmn;

-------------------------------------------------------------------------------
-- Copyright (c) 2003 Mentor Graphics Corporation
-------------------------------------------------------------------------------