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lc_matching.c
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lc_matching.c
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/*
* (c) Yury Kuchura
*
* This code can be used on terms of WTFPL Version 2 (http://www.wtfpl.net/).
*
* Heavily messed about with by OneOfEleven July 2020
* DiSlord adaptation to use on NanoVNA
*/
#ifdef __VNA_MEASURE_MODULE__
// Memory for measure cache data
static char measure_memory[128];
// Measure math functions
// quadratic function solver
static void match_quadratic_equation(float a, float b, float c, float *x)
{
const float a_x_2 = 2.0f * a;
const float d = (b * b) - (2.0f * a_x_2 * c);
if (d < 0){
x[0] = x[1] = 0.0f;
return;
}
const float sd = vna_sqrtf(d);
x[0] = (-b + sd) / a_x_2;
x[1] = (-b - sd) / a_x_2;
}
// Search functions
// Type of get value function
typedef float (*get_value_t)(uint16_t idx);
// Search point get_value(x) = y
// Used bilinear interpolation, return value = frequency of this point
#define MEASURE_SEARCH_LEFT -1
#define MEASURE_SEARCH_RIGHT 1
static float measure_search_value(uint16_t *idx, float y, get_value_t get, int16_t mode){
uint16_t x = *idx;
float y1, y2, y3;
y1 = y2 = y3 = get(x);
bool result = (y3 > y); // current position depend from start point
for(; x < sweep_points; x+=mode) {
y3 = get(x);
if(result != (y3 > y)) break;
y1 = y2;
y2 = y3;
}
if (x >= sweep_points) return 0;
x-=mode;
*idx = x;
// Now y1 > y, y2 > y, y3 <= y or y1 < y, y2 < y, y3 >= y
const float a = 0.5f * (y1 + y3) - y2;
const float b = 0.5f * (y3 - y1);
const float c = y2 - y;
float r[2];
match_quadratic_equation(a, b, c, r);
// Select result in middle 0 and 1 (in middle y2 and y3 result)
float res = (r[0] > 0 && r[0] < 1.0) ? r[0] : r[1];
// for search left need swap y1 and y3 points (use negative result)
if (mode < 0) res=-res;
return getFrequency(x) + getFrequencyStep() * res;
}
// Peak search, use bilinear interpolation for peak detect
#define MEASURE_SEARCH_MIN 0
#define MEASURE_SEARCH_MAX 1
static bool _greaterf(float x, float y) { return x > y; }
static bool _lesserf(float x, float y) { return x < y; }
static float search_peak_value(uint16_t *xp, get_value_t get, bool mode){
bool (*compare)(float x, float y) = mode ? _greaterf : _lesserf;
uint16_t x = 0;
float y2 = get(x), ytemp;
for(int i = 1; i < sweep_points; i++) {
if(compare(ytemp = get(i), y2)) {
y2 = ytemp;
x = i;
}
}
if (x < 1 || x >= sweep_points - 1) return y2;
*xp = x;
float y1 = get(x-1);
float y3 = get(x+1);
if (y1 == y3) return y2;
// const float a = 0.5f * (y1 + y3) - y2;
// const float b = 0.5f * (y3 - y1);
// const float c = y2;
// return c - b*b/(4*a);
const float a = 8*(y1 - 2*y2 + y3);
const float b = y3 - y1;
const float c = y2;
return c - b * b / a;
}
static float bilinear_interpolation(float y1, float y2, float y3, float k1){
const float a = 0.5f * (y1 + y3) - y2;
const float b = 0.5f * (y3 - y1);
const float c = y2;
return a * k1*k1 + b * k1 + c;
}
static bool measure_get_value(uint16_t ch, freq_t f, float *data){
if (f < frequency0 || f > frequency1)
return false;
// Search k1
uint16_t _points = sweep_points - 1;
freq_t span = frequency1 - frequency0;
uint32_t idx = (uint64_t)(f - frequency0) * (uint64_t)_points / span;
if (idx < 1 && idx > _points)
return false;
uint64_t v = (uint64_t)span * idx + _points/2;
freq_t src_f0 = frequency0 + (v ) / _points;
freq_t src_f1 = frequency0 + (v + span) / _points;
freq_t delta = src_f1 - src_f0;
float k1 = (delta == 0) ? 0.0 : (float)(f - src_f0) / delta;
#if 1
// Bilinear interpolation by k1
data[0] = bilinear_interpolation(measured[ch][idx-1][0], measured[ch][idx ][0], measured[ch][idx+1][0],k1);
data[1] = bilinear_interpolation(measured[ch][idx-1][1], measured[ch][idx ][1], measured[ch][idx+1][1],k1);
#else
// Linear Interpolate by k1
float k0 = 1.0 - k1;
data[0] = measured[ch][idx][0] * k0 + measured[ch][idx+1][0] * k1;
data[1] = measured[ch][idx][1] * k0 + measured[ch][idx+1][1] * k1;
#endif
return true;
}
#ifdef __USE_LC_MATCHING__
// calculate physical component values to match an impendace to 'ref_impedance' (ie 50R)
typedef struct
{
float xps; // Reactance parallel to source (can be NAN if not applicable)
float xs; // Serial reactance (can be 0.0 if not applicable)
float xpl; // Reactance parallel to load (can be NAN if not applicable)
} t_lc_match;
typedef struct
{
freq_t Hz;
float R0;
// L-Network solution structure
t_lc_match matches[4];
int16_t num_matches;
} lc_match_array_t;
// Size = 60 bytes
static lc_match_array_t *lc_match_array = (lc_match_array_t *)measure_memory;
// Calculate two solutions for ZL where (R + X * X / R) > R0
static void lc_match_calc_hi(float R0, float RL, float XL, t_lc_match *matches)
{
float xp[2];
const float a = R0 - RL;
const float b = 2.0f * XL * R0;
const float c = R0 * (XL * XL + RL * RL);
match_quadratic_equation(a, b, c, xp);
// found two impedances parallel to load
//
// now calculate serial impedances
const float RL1 = -XL * xp[0];
const float XL1 = RL * xp[0];
const float RL2 = RL;// + 0.0f;
const float XL2 = XL + xp[0];
matches[0].xs = (RL1 * XL2 - RL2 * XL1) / (RL2 * RL2 + XL2 * XL2);
matches[0].xps = 0.0f;
matches[0].xpl = xp[0];
const float RL3 = -XL * xp[1];
const float XL3 = RL * xp[1];
const float RL4 = RL;// + 0.0f;
const float XL4 = XL + xp[1];
matches[1].xs = (RL3 * XL4 - RL4 * XL3) / (RL4 * RL4 + XL4 * XL4);
matches[1].xps = 0.0f;
matches[1].xpl = xp[1];
}
// Calculate two solutions for ZL where R < R0
static void lc_match_calc_lo(float R0, float RL, float XL, t_lc_match *matches)
{
float xs[2];
// Calculate Xs
const float a = 1.0f;
const float b = 2.0f * XL;
const float c = RL * RL + XL * XL - R0 * RL;
match_quadratic_equation(a, b, c, xs);
// got two serial impedances that change ZL to the Y.real = 1/R0
//
// now calculate impedances parallel to source
const float RL1 = RL;// + 0.0f;
const float XL1 = XL + xs[0];
const float RL3 = RL1 * R0;
const float XL3 = XL1 * R0;
const float RL5 = RL1 - R0;
const float XL5 = XL1;// - 0.0f;
matches[0].xs = xs[0];
matches[0].xps = (RL5 * XL3 - RL3 * XL5) / (RL5 * RL5 + XL5 * XL5);
matches[0].xpl = 0.0f;
const float RL2 = RL;// + 0.0f;
const float XL2 = XL + xs[1];
const float RL4 = RL2 * R0;
const float XL4 = XL2 * R0;
const float RL6 = RL2 - R0;
const float XL6 = XL2;// - 0.0f;
matches[1].xs = xs[1];
matches[1].xps = (RL6 * XL4 - RL4 * XL6) / (RL6 * RL6 + XL6 * XL6);
matches[1].xpl = 0.0f;
}
static int lc_match_calc(int index)
{
const float R0 = lc_match_array->R0;
// compute the impedance at the chosen frequency
const float *coeff = measured[0][index];
const float RL = resistance(index, coeff);
const float XL = reactance(index, coeff);
if (RL <= 0.5f)
return -1;
const float q_factor = XL / RL;
const float vswr = swr(index, coeff);
// no need for any matching
if (vswr <= 1.1f || q_factor >= 100.0f)
return 0;
// only one solution is enough: just a serial reactance
// this gives SWR < 1.1 if R is within the range 0.91 .. 1.1 of R0
t_lc_match *matches = lc_match_array->matches;
if ((RL * 1.1f) > R0 && RL < (R0 * 1.1f)){
matches[0].xpl = 0.0f;
matches[0].xps = 0.0f;
matches[0].xs = -XL;
return 1;
}
if (RL >= R0)
{ // two Hi-Z solutions
lc_match_calc_hi(R0, RL, XL, &matches[0]);
return 2;
}
// compute Lo-Z solutions
lc_match_calc_lo(R0, RL, XL, &matches[0]);
if ((RL + (XL * q_factor)) <= R0)
return 2;
// two more Hi-Z solutions exist
lc_match_calc_hi(R0, RL, XL, &matches[2]);
return 4;
}
static void prepare_lc_match(uint8_t mode, uint8_t update_mask)
{
(void)mode;
(void)update_mask;
// Made calculation only one time for current sweep and frequency
freq_t freq = get_marker_frequency(active_marker);
if (freq == 0)// || lc_match_array->Hz == freq)
return;
lc_match_array->R0 = 50.0f;
lc_match_array->Hz = freq;
// compute the possible LC matches
lc_match_array->num_matches = lc_match_calc(markers[active_marker].index);
// Mark to redraw area under L/C match text
int n = lc_match_array->num_matches;
if (n < 0) n = 0;
invalidate_rect(STR_MEASURE_X , STR_MEASURE_Y,
STR_MEASURE_X + 3 * STR_MEASURE_WIDTH, STR_MEASURE_Y + (n + 2)*STR_MEASURE_HEIGHT);
}
//
static void lc_match_x_str(uint32_t FHz, float X, int xp, int yp)
{
if (isnan(X) || 0.0f == X || -0.0f == X)
return;
char type;
#if 0
float val;
if (X < 0.0f) {val = 1.0f / (2.0f * VNA_PI * FHz * -X); type = 'F';}
else {val = X / (2.0f * VNA_PI * FHz); type = 'H';}
#else
if (X < 0.0f) {X = -1.0 / X; type = 'F';}
else { type = 'H';}
float val = X / ((2.0f * VNA_PI) * FHz);
#endif
cell_printf(xp, yp, "%4.2F%c", val, type);
}
// Render L/C match to cell
static void draw_lc_match(int x0, int y0)
{
int xp = STR_MEASURE_X - x0;
int yp = STR_MEASURE_Y - y0;
cell_printf(xp, yp, "L/C match for source Z0 = %0.1f"S_OHM, lc_match_array->R0);
#if 0
yp += STR_MEASURE_HEIGHT;
cell_printf(xp, yp, "%qHz %0.1f %c j%0.1f"S_OHM, match_array->Hz, match_array->RL, (match_array->XL >= 0) ? '+' : '-', vna_fabsf(match_array->XL));
#endif
yp += STR_MEASURE_HEIGHT;
if (yp >= CELLHEIGHT) return;
if (lc_match_array->num_matches < 0)
cell_printf(xp, yp, "No LC match for this");
else if (lc_match_array->num_matches == 0)
cell_printf(xp, yp, "No need for LC match");
else {
cell_printf(xp , yp, "Src shunt" );
cell_printf(xp + STR_MEASURE_WIDTH, yp, "Series" );
cell_printf(xp + 2*STR_MEASURE_WIDTH, yp, "Load shunt");
for (int i = 0; i < lc_match_array->num_matches; i++){
yp += STR_MEASURE_HEIGHT;
if (yp >= CELLHEIGHT) return;
lc_match_x_str(lc_match_array->Hz, lc_match_array->matches[i].xps, xp , yp);
lc_match_x_str(lc_match_array->Hz, lc_match_array->matches[i].xs , xp + STR_MEASURE_WIDTH, yp);
lc_match_x_str(lc_match_array->Hz, lc_match_array->matches[i].xpl, xp + 2*STR_MEASURE_WIDTH, yp);
}
}
}
#endif // __USE_LC_MATCHING__
#ifdef __S21_MEASURE__
typedef struct {
char *header;
freq_t freq; // resonant frequency
freq_t freq1; // fp
float l;
float c;
float c1; // capacitor parallel
float r;
float q; // Q factor
// freq_t f1;
// freq_t f2;
// float tan45;
} s21_analysis_t;
static s21_analysis_t *s21_measure = (s21_analysis_t *)measure_memory;
static float s21pow2(uint16_t i) {
const float re = measured[1][i][0]; // S21 real
const float im = measured[1][i][1]; // S21 imaginary
return re*re+im*im; // S21^2
}
static float s21tan(uint16_t i) {
const float re = measured[1][i][0]; // S21 real
const float im = measured[1][i][1]; // S21 imaginary
return im/re; // tan(S21)
}
// Phase Shift Measurement
// https://www.mikrocontroller.net/attachment/473317/Crystal_Motional_Parameters.pdf
static void analysis_lcshunt(void) {
uint16_t xp = 0, x2;
s21_measure->header = "LC-SHUNT";
// Minimum search
float ypeak = search_peak_value(&xp, s21pow2, MEASURE_SEARCH_MIN);
// peak frequency, R
float att = vna_sqrtf(ypeak);
s21_measure->r = config._measure_r * att / (2 * (1 - att));
if(s21_measure->r < 0) return;
set_marker_index(0, xp);
float tan45 = config._measure_r/(config._measure_r + 4 * s21_measure->r);
// s21_measure->tan45 = tan45;
// -45 degree search at left
x2 = xp;
float f1 = measure_search_value(&x2, -tan45, s21tan, MEASURE_SEARCH_LEFT);
if (f1 == 0) return;
set_marker_index(1, x2);
// +45 degree search at right
x2 = xp;
float f2 = measure_search_value(&x2, tan45, s21tan, MEASURE_SEARCH_RIGHT);
if (f2 == 0) return;
set_marker_index(2, x2);
// L,C,Q calculations
float bw = f2 - f1;
float fpeak = vna_sqrtf(f2 * f1);
s21_measure->freq = fpeak;
s21_measure->q = fpeak / bw;
s21_measure->l = s21_measure->q * s21_measure->r / ((2 * VNA_PI) * fpeak);
s21_measure->c = 1 / ((2 * VNA_PI) * fpeak * s21_measure->q * s21_measure->r);
}
static void analysis_lcseries(void) {
uint16_t xp=0, x2;
s21_measure->header = "LC-SERIES";
// Peak value and it frequency index search
float ypeak = search_peak_value(&xp, s21pow2, MEASURE_SEARCH_MAX);
if (xp == 0) return; // peak not found
// motional resistance, Rm
s21_measure->r = 2 * config._measure_r * (1.0f / vna_sqrtf(ypeak) - 1.0f);
if(s21_measure->r < 0) return;
set_marker_index(0, xp);
const float tan45 = 1.0f; // tand(45) = 1.0f
// Lookup +45 phase at left of xp index
x2 = xp;
float f1 = measure_search_value(&x2, tan45, s21tan, MEASURE_SEARCH_LEFT);
if (f1 == 0) return; // not found
set_marker_index(1, x2);
// Lookup -45 phase at right of xp index
x2 = xp;
float f2 = measure_search_value(&x2, -tan45, s21tan, MEASURE_SEARCH_RIGHT);
if (f2 == 0) return; // not found
set_marker_index(2, x2);
// L,C,Q calculation
float bw = f2 - f1;
float fpeak = vna_sqrtf(f2*f1);
// The total resistance, REFF, seen by the crystal is the sum of the load resistance (input and output) and the motional resistance, Rm:
float reff = 2 * config._measure_r + s21_measure->r;
s21_measure->freq = fpeak;
s21_measure->l = reff / ((2 * VNA_PI) * bw);
s21_measure->c = bw / ((2 * VNA_PI) * fpeak * fpeak * reff);
// q = 2*pi * Fp * Ls / R
s21_measure->q = (2 * VNA_PI) * fpeak * s21_measure->l / s21_measure->r;
// s21_measure->f1 = f1;
// s21_measure->f2 = f2;
}
static void analysis_xtalseries(void) {
analysis_lcseries();
s21_measure->header = "XTAL-SERIES";
// search S21 min
uint16_t xp=0;
search_peak_value(&xp, s21pow2, MEASURE_SEARCH_MIN);
if (xp == 0) return;
set_marker_index(3, xp);
freq_t freq1 = getFrequency(xp);
if(freq1 < s21_measure->freq) return;
s21_measure->freq1 = freq1;
// df = f * c / (2*c1) => c1 = f * c / (2*df)
s21_measure->c1 = s21_measure->c * s21_measure->freq / (2*(s21_measure->freq1 - s21_measure->freq));
}
static void draw_serial_result(int x0, int y0){
int xp = STR_MEASURE_X - x0;
int yp = STR_MEASURE_Y - y0;
cell_printf(xp, yp, s21_measure->header);
if (s21_measure->freq == 0 && s21_measure->freq1 == 0) {
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Not found");
return;
}
if (s21_measure->freq)
{
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Fs=%qHz", s21_measure->freq);
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Ls=%FH Cs=%FF Rs=%F" S_OHM, s21_measure->l, s21_measure->c, s21_measure->r);
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Q=%.3f", s21_measure->q);
// cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "tan45=%.4f", s21_measure->tan45);
// cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "F1=%qHz F2=%qHz", s21_measure->f1, s21_measure->f2);
}
if (s21_measure->freq1){
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Fp=%qHz", s21_measure->freq1);
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Cp=%FF", s21_measure->c1);
}
}
static void prepare_series(uint8_t type, uint8_t update_mask)
{
(void)update_mask;
uint16_t n;
// for detect completion
s21_measure->freq = 0;
s21_measure->freq1 = 0;
switch (type){
case MEASURE_SHUNT_LC: n = 4; analysis_lcshunt(); break;
case MEASURE_SERIES_LC: n = 4; analysis_lcseries(); break;
case MEASURE_SERIES_XTAL: n = 6; analysis_xtalseries(); break;
default: return;
}
// Prepare for update
invalidate_rect(STR_MEASURE_X , STR_MEASURE_Y,
STR_MEASURE_X + 3 * STR_MEASURE_WIDTH, STR_MEASURE_Y + n * STR_MEASURE_HEIGHT);
markmap_all_markers();
}
#endif // __S21_MEASURE__
#ifdef __S11_CABLE_MEASURE__
typedef struct {
float R;
float len;
float loss;
float C0;
float a, b, c;
} s11_cable_measure_t;
static s11_cable_measure_t *s11_cable = (s11_cable_measure_t *)measure_memory;
static float s11imag(uint16_t i) {
return measured[0][i][1];
}
static void draw_s11_cable(int x0, int y0){
int xp = STR_MEASURE_X - x0;
int yp = STR_MEASURE_Y - y0;
cell_printf(xp, yp, "S11 CABLE");
if (s11_cable->R){
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Z0 = %F" S_OHM, s11_cable->R);
// cell_printf(xp, yp+=FONT_STR_HEIGHT, "C0 = %FF", s11_cable->C0);
}
if (s11_cable->len)
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Length = %Fm (K=%d%%)", s11_cable->len, velocity_factor);
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Loss = %FdB", s11_cable->loss);
}
static void prepare_s11_cable(uint8_t type, uint8_t update_mask)
{
(void)type;
freq_t f1;
if (update_mask & MEASURE_UPD_SWEEP) {
s11_cable->R = 0.0f;
s11_cable->len = 0.0f;
uint16_t x = 0;
f1 = measure_search_value(&x, 0, s11imag, MEASURE_SEARCH_RIGHT);
if (f1){
s11_cable->len = velocity_factor * (SPEED_OF_LIGHT / 400.0f) / f1;
float data[2];
if (measure_get_value(0, f1/2, data)){
s11_cable->R = vna_fabsf(reactance(0, data));
// s11_cable->C0 = velocity_factor / (100.0f * SPEED_OF_LIGHT * s11_cable->R);
}
}
}
if ((update_mask & MEASURE_UPD_ALL) && active_marker != MARKER_INVALID) {
int idx = markers[active_marker].index;
s11_cable->loss = vna_fabsf(logmag(idx, measured[0][idx]) / 2);
}
// Prepare for update
invalidate_rect(STR_MEASURE_X , STR_MEASURE_Y,
STR_MEASURE_X + 3 * STR_MEASURE_WIDTH, STR_MEASURE_Y + 4 * STR_MEASURE_HEIGHT);
}
#endif // __S11_CABLE_MEASURE__
#ifdef __S11_RESONANCE_MEASURE__
#define MEASURE_RESONANCE_COUNT 6
typedef struct {
struct {
freq_t f;
float r;
float x;
} data[MEASURE_RESONANCE_COUNT];
uint8_t count;
} s11_resonance_measure_t;
static s11_resonance_measure_t *s11_resonance = (s11_resonance_measure_t *)measure_memory;
static float s11_resonance_value(uint16_t i) {
return measured[0][i][1];
}
static float s11_resonance_min(uint16_t i) {
return fabsf(reactance(i, measured[0][i]));
}
static void draw_s11_resonance(int x0, int y0){
int xp = STR_MEASURE_X - x0;
int yp = STR_MEASURE_Y - y0;
cell_printf(xp, yp, "S11 RESONANCE");
if (s11_resonance->count == 0) {
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "Not found");
return;
}
for (int i = 0; i < s11_resonance->count; i++)
cell_printf(xp, yp+=STR_MEASURE_HEIGHT, "%qHz, %F%+jF" S_OHM, s11_resonance->data[i].f, s11_resonance->data[i].r, s11_resonance->data[i].x);
}
static bool add_resonance_value(int i, uint16_t x, freq_t f) {
float data[2];
if (measure_get_value(0, f, data)) {
s11_resonance->data[i].f = f;
//set_marker_index(i, x);
s11_resonance->data[i].r = resistance(x, data);
s11_resonance->data[i].x = reactance(x, data);
return true;
}
return false;
}
static void prepare_s11_resonance(uint8_t type, uint8_t update_mask)
{
(void)type;
if (update_mask & MEASURE_UPD_SWEEP) {
int i;
freq_t f;
uint16_t x = 0;
// Search resonances (X == 0)
for (i = 0; i < MEASURE_RESONANCE_COUNT && i < MARKERS_MAX;) {
f = measure_search_value(&x, 0.0f, s11_resonance_value, MEASURE_SEARCH_RIGHT);
if (f == 0) break;
if (add_resonance_value(i, x, f))
i++;
x++;
}
if (i == 0) { // Search minimum position, if resonances not found
x = 0;
search_peak_value(&x, s11_resonance_min, MEASURE_SEARCH_MIN);
if (x && add_resonance_value(0, x, getFrequency(x)))
i = 1;
}
s11_resonance->count = i;
}
// Prepare for update
invalidate_rect(STR_MEASURE_X , STR_MEASURE_Y,
STR_MEASURE_X + 3 * STR_MEASURE_WIDTH, STR_MEASURE_Y + (MEASURE_RESONANCE_COUNT + 1) * STR_MEASURE_HEIGHT);
}
#endif //__S11_RESONANCE_MEASURE__
#endif // __VNA_MEASURE__