diff --git a/figs/force_sen_steps_time_domain_par_R.pdf b/figs/force_sen_steps_time_domain_par_R.pdf new file mode 100644 index 0000000..02242e0 Binary files /dev/null and b/figs/force_sen_steps_time_domain_par_R.pdf differ diff --git a/figs/force_sen_steps_time_domain_par_R.png b/figs/force_sen_steps_time_domain_par_R.png new file mode 100644 index 0000000..8f2c926 Binary files /dev/null and b/figs/force_sen_steps_time_domain_par_R.png differ diff --git a/index.html b/index.html index 5b1c3c8..fc9bdca 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Encoder - Test Bench @@ -35,49 +35,50 @@

Table of Contents

-
-

1 Experimental Setup

+
+

1 Experimental Setup

-The experimental Setup is schematically represented in Figure 1. +The experimental Setup is schematically represented in Figure 1.

@@ -86,21 +87,21 @@ The displacement of the mass (relative to the mechanical frame) is measured both

-
+

exp_setup_schematic.png

Figure 1: Schematic of the Experiment

-
+

IMG_20201023_153905.jpg

Figure 2: Side View of the encoder

-
+

IMG_20201023_153914.jpg

Figure 3: Front View of the encoder

@@ -108,8 +109,8 @@ The displacement of the mass (relative to the mechanical frame) is measured both
-
-

2 Huddle Test

+
+

2 Huddle Test

The goal in this section is the estimate the noise of both the encoder and the intereferometer. @@ -121,8 +122,8 @@ Ideally, a mechanical part would clamp the two together, we here suppose that th

-
-

2.1 Load Data

+
+

2.1 Load Data

load('mat/int_enc_huddle_test.mat', 'interferometer', 'encoder', 't');
@@ -137,11 +138,11 @@ encoder = detrend(encoder, 0);
-
-

2.2 Time Domain Results

+
+

2.2 Time Domain Results

-
+

huddle_test_time_domain.png

Figure 4: Huddle test - Time domain signals

@@ -153,7 +154,7 @@ encoder = detrend(encoder, 0);
-
+

huddle_test_time_domain_filtered.png

Figure 5: Huddle test - Time domain signals filtered with a LPF at 10Hz

@@ -161,8 +162,8 @@ encoder = detrend(encoder, 0);
-
-

2.3 Frequency Domain Noise

+
+

2.3 Frequency Domain Noise

Ts = 1e-4;
@@ -174,7 +175,7 @@ win = hann(ceil(10/Ts));
-
+

huddle_test_asd.png

Figure 6: Amplitude Spectral Density of the signals during the Huddle test

@@ -183,8 +184,8 @@ win = hann(ceil(10/Ts));
-
-

3 Comparison Interferometer / Encoder

+
+

3 Comparison Interferometer / Encoder

The goal here is to make sure that the interferometer and encoder measurements are coherent. @@ -192,8 +193,8 @@ We may see non-linearity in the interferometric measurement.

-
-

3.1 Load Data

+
+

3.1 Load Data

load('mat/int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't');
@@ -209,18 +210,18 @@ u = detrend(u, 0);
-
-

3.2 Time Domain Results

+
+

3.2 Time Domain Results

-
+

int_enc_one_cycle.png

Figure 7: One cycle measurement

-
+

int_enc_one_cycle_error.png

Figure 8: Difference between the Encoder and the interferometer during one cycle

@@ -228,8 +229,8 @@ u = detrend(u, 0);
-
-

3.3 Difference between Encoder and Interferometer as a function of time

+
+

3.3 Difference between Encoder and Interferometer as a function of time

Ts = 1e-4;
@@ -250,7 +251,7 @@ d_err_mean = d_err_mean - mean(d_err_mean);
-
+

int_enc_error_mean_time.png

Figure 9: Difference between the two measurement in the time domain, averaged for all the cycles

@@ -258,8 +259,8 @@ d_err_mean = d_err_mean - mean(d_err_mean);
-
-

3.4 Difference between Encoder and Interferometer as a function of position

+
+

3.4 Difference between Encoder and Interferometer as a function of position

Compute the mean of the interferometer measurement corresponding to each of the encoder measurement. @@ -278,7 +279,7 @@ i_mean_error = (i_mean - e_sorted);

-
+

int_enc_error_mean_position.png

Figure 10: Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles

@@ -299,7 +300,7 @@ e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init +

int_non_linearity_period_wavelength.png

Figure 11: Non-Linearity of the Interferometer over the period of the wavelength

@@ -308,12 +309,12 @@ e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init -

4 Identification

+
+

4 Identification

-
-

4.1 Load Data

+
+

4.1 Load Data

load('mat/int_enc_id_noise_bis.mat', 'interferometer', 'encoder', 'u', 't');
@@ -329,8 +330,8 @@ u = detrend(u, 0);
-
-

4.2 Identification

+
+

4.2 Identification

Ts = 1e-4; % Sampling Time [s]
@@ -348,14 +349,14 @@ win = hann(ceil(10/Ts));
-
+

identification_dynamics_coherence.png

-
+

identification_dynamics_bode.png

@@ -363,12 +364,12 @@ win = hann(ceil(10/Ts));
-
-

5 Change of Stiffness due to Sensors stack being open/closed circuit

+
+

5 Change of Stiffness due to Sensors stack being open/closed circuit

-
-

5.1 Load Data

+
+

5.1 Load Data

oc = load('./mat/identification_open_circuit.mat', 't', 'encoder', 'u');
@@ -378,8 +379,8 @@ sc = load('./mat/identification_short_circuit.mat'
-
-

5.2 Transfer Functions

+
+

5.2 Transfer Functions

Ts = 1e-4; % Sampling Time [s]
@@ -397,26 +398,26 @@ win = hann(ceil(10/Ts));
-
+

stiffness_force_sensor_coherence.png

-
+

stiffness_force_sensor_bode.png

-
+

stiffness_force_sensor_bode_zoom.png

Figure 16: Zoom on the change of resonance

-
+

The change of resonance frequency / stiffness is very small and is not important here.

@@ -426,8 +427,8 @@ The change of resonance frequency / stiffness is very small and is not important
-
-

6 Generated Number of Charge / Voltage

+
+

6 Generated Number of Charge / Voltage

Two stacks are used as actuator (in parallel) and one stack is used as sensor. @@ -438,8 +439,8 @@ The amplifier gain is 20V/V (Cedrat LA75B).

-
-

6.1 Steps

+
+

6.1 Steps

load('./mat/force_sensor_steps.mat', 't', 'encoder', 'u', 'v');
@@ -459,7 +460,7 @@ xlabel('Time [s]'); ylabel(
+

 
force_sen_steps_time_domain.png
 

 
Figure 17: Time domain signal during the 3 actuator voltage steps

@@ -468,11 +469,12 @@ xlabel('Time [s]'); ylabel(
-
  • 2.5, 23
    • 
-
  • 23.8, 35
    • 
-
  • 35.8, 50
    • 
-
+
    
+
    t_s = [ 2.5, 23;
+       23.8, 35;
+       35.8, 50];
+
    
+
    
 
 
    
 Fit function:
@@ -485,52 +487,25 @@ Fit function:
 
    
 We are interested by the b(2) term, which is the time constant of the exponential.
 
    
-
 
    
-
    tau = zeros(3,1);
-V0  = zeros(3,1);
+
    tau = zeros(size(t_s, 1),1);
+V0  = zeros(size(t_s, 1),1);
 
    
 
    
 
 
    
-
    t_cur = t(2.5 < t & t < 23);
-t_cur = t_cur - t_cur(1);
-y_cur = v(2.5 < t & t < 23);
+
    for t_i = 1:size(t_s, 1)
+    t_cur = t(t_s(t_i, 1) < t & t < t_s(t_i, 2));
+    t_cur = t_cur - t_cur(1);
+    y_cur = v(t_s(t_i, 1) < t & t < t_s(t_i, 2));
 
-nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
-B0 = [0.5, -0.15, 2.2];                        % Choose Appropriate Initial Estimates
-[B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
+    nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
+    B0 = [0.5, -0.15, 2.2];                        % Choose Appropriate Initial Estimates
+    [B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
 
-tau(1) = 1/B(2);
-V0(1)  = B(3);
-
    
-
    
-
-
    
-
    t_cur = t(23.8 < t & t < 35);
-t_cur = t_cur - t_cur(1);
-y_cur = v(23.8 < t & t < 35);
-
-nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
-B0 = [0.5, -0.15, 2.2];                 % Choose Appropriate Initial Estimates
-[B,rnrm] = fminsearch(nrmrsd, B0);      % Estimate Parameters ‘B’
-
-tau(2) = 1/B(2);
-V0(2)  = B(3);
-
    
-
    
-
-
    
-
    t_cur = t(35.8 < t);
-t_cur = t_cur - t_cur(1);
-y_cur = v(35.8 < t);
-
-nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
-B0 = [0.5, -0.15, 2.2];                 % Choose Appropriate Initial Estimates
-[B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
-
-tau(3) = 1/B(2);
-V0(3)  = B(3);
+    tau(t_i) = 1/B(2);
+    V0(t_i)  = B(3);
+end
 
    
 
    
 
@@ -584,7 +559,7 @@ Rin = abs(mean(tau))/Cp;
 The input impedance of the Speedgoat’s ADC should then be close to \(1.5\,M\Omega\) (specified at \(1\,M\Omega\)).
 
    
 
-
    
+
    
 
    
 How can we explain the voltage offset?
 
    
@@ -592,11 +567,11 @@ How can we explain the voltage offset?
 
    
 
 
    
-As shown in Figure 18 (taken from (Reza and Andrew 2006)), an input voltage offset is due to the input bias current \(i_n\).
+As shown in Figure 18 (taken from (Reza and Andrew 2006)), an input voltage offset is due to the input bias current \(i_n\).
 
    
 
 
-
    
+
    
 
    piezo_sensor_model_instrumentation.png
 
    
 
    Figure 18: Model of a piezoelectric transducer (left) and instrumentation amplifier (right)
    
@@ -632,7 +607,7 @@ If we allow the high pass corner frequency to be equals to 3Hz:
 
    
 
    
 
    fc = 3;
-Ra = Rin/(fc*C*Rin - 1);
+Ra = Rin/(fc*Cp*Rin - 1);
 
    
 
    
 
@@ -660,9 +635,178 @@ Which is much more acceptable.
 
    
 
    
 
-
    
-
    6.2 Sinus
    
+
    
+
    6.2 Add Parallel Resistor
    
 
    
+
    
+A resistor of \(\approx 100\,k\Omega\) is added in parallel with the force sensor and the same kin.
+
    
+
+
    
+
    load('./mat/force_sensor_steps_R_82k7.mat', 't', 'encoder', 'u', 'v');
+
    
+
    
+
+
    
+
    figure;
+tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+nexttile;
+plot(t, v);
+xlabel('Time [s]'); ylabel('Measured voltage [V]');
+nexttile;
+plot(t, u);
+xlabel('Time [s]'); ylabel('Actuator Voltage [V]');
+
    
+
    
+
+
+
    
+
    force_sen_steps_time_domain_par_R.png
+
    
+
    Figure 19: Time domain signal during the actuator voltage steps
    
+
    
+
+
    
+Three steps are performed at the following time intervals:
+
    
+
    
+
    t_s = [1.9,  6;
+       8.5, 13;
+      15.5, 21;
+      22.6, 26;
+      30.0, 36;
+      37.5, 41;
+      46.2, 49.5]
+
    
+
    
+
+
    
+Fit function:
+
    
+
    
+
    f = @(b,x) b(1).*exp(b(2).*x) + b(3);
+
    
+
    
+
+
    
+We are interested by the b(2) term, which is the time constant of the exponential.
+
    
+
+
    
+
    tau = zeros(size(t_s, 1),1);
+V0  = zeros(size(t_s, 1),1);
+
    
+
    
+
+
    
+
    for t_i = 1:size(t_s, 1)
+    t_cur = t(t_s(t_i, 1) < t & t < t_s(t_i, 2));
+    t_cur = t_cur - t_cur(1);
+    y_cur = v(t_s(t_i, 1) < t & t < t_s(t_i, 2));
+
+    nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
+    B0 = [0.5, -0.2, 0.2];                        % Choose Appropriate Initial Estimates
+    [B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
+
+    tau(t_i) = 1/B(2);
+    V0(t_i)  = B(3);
+end
+
    
+
    
+
+
    
+And indeed, we obtain a much smaller offset voltage and a much faster time constant.
+
    
+
+
+
+
+++
++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    



    \(tau\) [s]\(V_0\) [V]
    0.430.15
    0.450.16
    0.430.15
    0.430.15
    0.450.15
    0.460.16
    0.480.16
    
+
+
    
+Knowing the capacitance value, we can estimate the value of the added resistor (neglecting the input impedance of \(\approx 1\,M\Omega\)):
+
    
+
+
    
+
    Cp = 4.4e-6; % [F]
+Rin = abs(mean(tau))/Cp;
+
    
+
    
+
+
    +101200.0
+
    
+
+
+
    
+And we can verify that the bias current estimation stays the same:
+
    
+
    
+
    in = mean(V0)/Rin;
+
    
+
    
+
+
    +1.5305e-06
+
    
+
+
+
    
+This validates the model of the ADC and the effectiveness of the added resistor.
+
    
+
    
+
    
+
+
    
+
    6.3 Sinus
    
+
    
 
    
 
    load('./mat/force_sensor_sin.mat', 't', 'encoder', 'u', 'v');
 
@@ -674,14 +818,14 @@ t       = t(t>25);
 
    
 
 
    
-The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure 19).
+The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure 20).
 
    
 
 
-
    
+
    
 
    force_sensor_sin_u.png
 
    
-
    Figure 19: Driving Voltage
    
+
    Figure 20: Driving Voltage
    
 
    
 
 
    
@@ -698,14 +842,14 @@ The full stroke as measured by the encoder is:
 
 
 
    
-Its signal is shown in Figure 20.
+Its signal is shown in Figure 21.
 
    
 
 
-
    
+
    
 
    force_sensor_sin_encoder.png
 
    
-
    Figure 20: Encoder measurement
    
+
    Figure 21: Encoder measurement
    
 
    
 
 
    
@@ -713,10 +857,10 @@ The generated voltage by the stack is shown in Figure
 
    
 
 
-
    
+
    
 
    force_sensor_sin_stack.png
 
    
-
    Figure 21: Voltage measured on the stack used as a sensor
    
+
    Figure 22: Voltage measured on the stack used as a sensor
    
 
    
 
 
    
@@ -728,18 +872,18 @@ The capacitance of the stack is
 
    
 
 
    
-The corresponding generated charge is then shown in Figure 22.
+The corresponding generated charge is then shown in Figure 23.
 
    
 
-
    
+
    
 
    force_sensor_sin_charge.png
 
    
-
    Figure 22: Generated Charge
    
+
    Figure 23: Generated Charge
    
 
    
 
 
 
    
-The relation between the generated voltage and the measured displacement is almost linear as shown in Figure 23.
+The relation between the generated voltage and the measured displacement is almost linear as shown in Figure 24.
 
    
 
 
    
@@ -748,10 +892,10 @@ The relation between the generated voltage and the measured displacement is almo
 
    
 
 
-
    
+
    
 
    force_sensor_linear_relation.png
 
    
-
    Figure 23: Almost linear relation between the relative displacement and the generated voltage
    
+
    Figure 24: Almost linear relation between the relative displacement and the generated voltage
    
 
    
 
 
    
@@ -777,7 +921,7 @@ With a 16bits ADC, the resolution will then be equals to (in [nm]):
 
    
 
    
 
    Author: Dehaeze Thomas
    
-
    Created: 2020-10-29 jeu. 10:08
    
+
    Created: 2020-11-04 mer. 20:38
    
 
    
 
 
diff --git a/index.org b/index.org
index a3426e7..d3349ba 100644
--- a/index.org
+++ b/index.org
@@ -551,9 +551,11 @@ The amplifier gain is 20V/V (Cedrat LA75B).
 [[file:figs/force_sen_steps_time_domain.png]]
 
 Three steps are performed at the following time intervals:
-- 2.5, 23
-- 23.8, 35
-- 35.8, 50
+#+begin_src matlab
+  t_s = [ 2.5, 23;
+         23.8, 35;
+         35.8, 50];
+#+end_src
 
 Fit function:
 #+begin_src matlab
@@ -561,49 +563,24 @@ Fit function:
 #+end_src
 
 We are interested by the =b(2)= term, which is the time constant of the exponential.
-
 #+begin_src matlab
-  tau = zeros(3,1);
-  V0  = zeros(3,1);
+  tau = zeros(size(t_s, 1),1);
+  V0  = zeros(size(t_s, 1),1);
 #+end_src
 
 #+begin_src matlab
-  t_cur = t(2.5 < t & t < 23);
-  t_cur = t_cur - t_cur(1);
-  y_cur = v(2.5 < t & t < 23);
+  for t_i = 1:size(t_s, 1)
+      t_cur = t(t_s(t_i, 1) < t & t < t_s(t_i, 2));
+      t_cur = t_cur - t_cur(1);
+      y_cur = v(t_s(t_i, 1) < t & t < t_s(t_i, 2));
 
-  nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
-  B0 = [0.5, -0.15, 2.2];                        % Choose Appropriate Initial Estimates
-  [B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
+      nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
+      B0 = [0.5, -0.15, 2.2];                        % Choose Appropriate Initial Estimates
+      [B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
 
-  tau(1) = 1/B(2);
-  V0(1)  = B(3);
-#+end_src
-
-#+begin_src matlab
-  t_cur = t(23.8 < t & t < 35);
-  t_cur = t_cur - t_cur(1);
-  y_cur = v(23.8 < t & t < 35);
-
-  nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
-  B0 = [0.5, -0.15, 2.2];                 % Choose Appropriate Initial Estimates
-  [B,rnrm] = fminsearch(nrmrsd, B0);      % Estimate Parameters ‘B’
-
-  tau(2) = 1/B(2);
-  V0(2)  = B(3);
-#+end_src
-
-#+begin_src matlab
-  t_cur = t(35.8 < t);
-  t_cur = t_cur - t_cur(1);
-  y_cur = v(35.8 < t);
-
-  nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
-  B0 = [0.5, -0.15, 2.2];                 % Choose Appropriate Initial Estimates
-  [B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
-
-  tau(3) = 1/B(2);
-  V0(3)  = B(3);
+      tau(t_i) = 1/B(2);
+      V0(t_i)  = B(3);
+  end
 #+end_src
 
 #+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
@@ -665,7 +642,7 @@ An additional resistor in parallel with $R_{in}$ would have two effects:
 If we allow the high pass corner frequency to be equals to 3Hz:
 #+begin_src matlab
   fc = 3;
-  Ra = Rin/(fc*C*Rin - 1);
+  Ra = Rin/(fc*Cp*Rin - 1);
 #+end_src
 
 #+begin_src matlab :results value replace :exports results
@@ -689,6 +666,116 @@ With this parallel resistance value, the voltage offset would be:
 
 Which is much more acceptable.
 
+** Add Parallel Resistor
+A resistor of $\approx 100\,k\Omega$ is added in parallel with the force sensor and the same kin.
+
+#+begin_src matlab
+  load('./mat/force_sensor_steps_R_82k7.mat', 't', 'encoder', 'u', 'v');
+#+end_src
+
+#+begin_src matlab
+  figure;
+  tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+  nexttile;
+  plot(t, v);
+  xlabel('Time [s]'); ylabel('Measured voltage [V]');
+  nexttile;
+  plot(t, u);
+  xlabel('Time [s]'); ylabel('Actuator Voltage [V]');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+  exportFig('figs/force_sen_steps_time_domain_par_R.pdf', 'width', 'wide', 'height', 'tall');
+#+end_src
+
+#+name: fig:force_sen_steps_time_domain_par_R
+#+caption: Time domain signal during the actuator voltage steps
+#+RESULTS:
+[[file:figs/force_sen_steps_time_domain_par_R.png]]
+
+Three steps are performed at the following time intervals:
+#+begin_src matlab
+  t_s = [1.9,  6;
+         8.5, 13;
+        15.5, 21;
+        22.6, 26;
+        30.0, 36;
+        37.5, 41;
+        46.2, 49.5]
+#+end_src
+
+Fit function:
+#+begin_src matlab
+  f = @(b,x) b(1).*exp(b(2).*x) + b(3);
+#+end_src
+
+We are interested by the =b(2)= term, which is the time constant of the exponential.
+
+#+begin_src matlab
+  tau = zeros(size(t_s, 1),1);
+  V0  = zeros(size(t_s, 1),1);
+#+end_src
+
+#+begin_src matlab
+  for t_i = 1:size(t_s, 1)
+      t_cur = t(t_s(t_i, 1) < t & t < t_s(t_i, 2));
+      t_cur = t_cur - t_cur(1);
+      y_cur = v(t_s(t_i, 1) < t & t < t_s(t_i, 2));
+
+      nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
+      B0 = [0.5, -0.2, 0.2];                        % Choose Appropriate Initial Estimates
+      [B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
+
+      tau(t_i) = 1/B(2);
+      V0(t_i)  = B(3);
+  end
+#+end_src
+
+And indeed, we obtain a much smaller offset voltage and a much faster time constant.
+
+#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
+  data2orgtable([abs(tau), V0], {}, {'$tau$ [s]', '$V_0$ [V]'}, ' %.2f ');
+#+end_src
+
+#+RESULTS:
+| $tau$ [s] | $V_0$ [V] |
+|-----------+-----------|
+|      0.43 |      0.15 |
+|      0.45 |      0.16 |
+|      0.43 |      0.15 |
+|      0.43 |      0.15 |
+|      0.45 |      0.15 |
+|      0.46 |      0.16 |
+|      0.48 |      0.16 |
+
+Knowing the capacitance value, we can estimate the value of the added resistor (neglecting the input impedance of $\approx 1\,M\Omega$):
+
+#+begin_src matlab
+  Cp = 4.4e-6; % [F]
+  Rin = abs(mean(tau))/Cp;
+#+end_src
+
+#+begin_src matlab :results value replace :exports results
+  ans = Rin
+#+end_src
+
+#+RESULTS:
+: 101200.0
+
+And we can verify that the bias current estimation stays the same:
+#+begin_src matlab
+  in = mean(V0)/Rin;
+#+end_src
+
+#+begin_src matlab :results value replace :exports results
+   ans = in
+#+end_src
+
+#+RESULTS:
+: 1.5305e-06
+
+This validates the model of the ADC and the effectiveness of the added resistor.
+
 ** Sinus
 #+begin_src matlab
   load('./mat/force_sensor_sin.mat', 't', 'encoder', 'u', 'v');