remove empty bibliography

content/zettels/transconductance_amplifiers.md

@@ -57,7 +57,7 @@ Such amplifier is used to control motors (e.g. voice coil, BLDC, stepper motors,
 
 ## Required properties {#required-properties}
 
-Main required properties are (taken from (<a href="#citeproc_bib_item_4">Schmidt, Schitter, and Rankers 2020</a>)):
+Main required properties are (taken from (<a href="#citeproc_bib_item_2">Schmidt, Schitter, and Rankers 2020</a>)):
 
 -   **Power delivery capability**
 -   **Dynamic properties**
@@ -221,69 +221,20 @@ Howland current source is shown in [Figure 1](#figure--fig:art-electronics-curre
 
 <a id="figure--fig:art-electronics-current-source"></a>
 
-{{< figure src="/ox-hugo/art_electronics_current_source.png" caption="<span class='figure-number'>Figure 1: </span>From (<a href='#citeproc_bib_item_1'>Horowitz 2015</a>)" >}}
+{{< figure src="/ox-hugo/art_electronics_current_source.png" caption="<span class='figure-number'>Figure 1: </span>From <&horowitz15_art_of_elect_third_edition>" >}}
 
 
 ### Other circuits found in the litterature {#other-circuits-found-in-the-litterature}
 
-{{< figure src="/ox-hugo/lafarga24_current_amplifier.png" caption="<span class='figure-number'>Figure 2: </span>From (<a href='#citeproc_bib_item_2'>Lafarga 2024</a>), Appendix B" >}}
+{{< figure src="/ox-hugo/lafarga24_current_amplifier.png" caption="<span class='figure-number'>Figure 2: </span>From <&lafarga24_activ_vibrat_isolat_system_space_applic>, Appendix B" >}}
 
-{{< figure src="/ox-hugo/okyay16_current_amplifier_schematic.png" caption="<span class='figure-number'>Figure 3: </span>From (<a href='#citeproc_bib_item_3'>Okyay 2016</a>), Appendix A" >}}
+{{< figure src="/ox-hugo/okyay16_current_amplifier_schematic.png" caption="<span class='figure-number'>Figure 3: </span>From <&okyay16_mechat_desig_dynam_contr_metrol>, Appendix A" >}}
 
 
 ## Estimation of the required current noise {#estimation-of-the-required-current-noise}
 
-
-### Voice Coil Actuator with flexible guiding {#voice-coil-actuator-with-flexible-guiding}
-
-```matlab
-%% Frequency vector used for the analysis
-freqs = logspace(0, 4, 1000); % [Hz]
-
-%% Motor properties
-Kt = 28; % Force constant [N/A]
-
-%% Amplifier Noise
-In = 1e-6.*ones(size(freqs)); % Current noise density [A/sqrt(Hz)]
-
-%% DAC Noise
-Vn = (20/2^20)^2/12*1e4*ones(size(freqs)); % DAC output noise in [V/sqrt(Hz)]
-Vn = 3e-8
-Gi = 0.2; % Amplifier Gain [A/V]
-
-%% Mechanical properties
-m = 200e-3; % Mobile mass [kg]
-k = 1e3; % Guiding stiffness [N/m]
-xi = 0.05; % Modal Damping
-```
-
-```matlab
-%% Transfer function from F [N] to x [m]
-Gx = 1/(m*s^2);
-```
-
-```matlab
-%% Transfer function from I [A] to x [m]
-x_asd_i = In.*abs(squeeze(freqresp(Gx*Kt, freqs, 'Hz')))';
-x_asd_v = Vn.*abs(squeeze(freqresp(Gx*Gi*Kt, freqs, 'Hz')))';
-
-%% Cumulative amplitude spectrum
-figure;
-tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
-
-nexttile();
-hold on;
-plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(x_asd_i.^2)))) , '-');
-plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(x_asd_v.^2)))) , '-');
-plot(freqs, ex , '-');
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Magnitude'); xlabel('Frequency [Hz]');
-xlim([0, 1e3]);
-```
-
-
-### Approximate analytical formula {#approximate-analytical-formula}
+Let's consider a simple suspended mass (with mass `m` in kg) driven by a voice coil (with a motor constant `Kt` in N/A).
+The control is done in closed-loop, with a feedback bandwidth `fb` in Hz.
 
 Parameters:
 
@@ -304,40 +255,32 @@ We have that the residual motion when the feedback controller is closed is appro
 
 Therefore, this formula can be used to:
 
--
-
-<!--listend-->
-
 ```matlab
 %% Estimate the position stability from the current noise and system parameters
-m = 1; % [kg]
+m  = 1; % [kg]
 In = 1e-6; % [A/sqrt(Hz)]
 Kt = 10; % [N/A]
-fb = 10; % [Hz]
+fb = 100; % [Hz]
 
 ex = In*Kt/m/(2*pi)^2*sqrt(1./(3*fb^3));
 ```
 
 ```text
-epsilon x = 4.6 [nm RMS]
+epsilon x = 0.15 [nm RMS]
 ```
 
--
-
-<!--listend-->
-
 ```matlab
 %% Estimate the required current noise from the wanted position stability and the parameters of the system
-m = 1; % [kg]
+m  = 1; % [kg]
 Kt = 10; % [N/A]
-fb = 50; % [Hz]
+fb = 100; % [Hz]
 ex = 1e-9; % [m RMS]
 
 In = ex*m*(2*pi)^2/Kt * sqrt(3*fb^3);
 ```
 
 ```text
-In = 2.4e-06 [A/sqrt(Hz)]
+In = 6.8e-06 [A/sqrt(Hz)]
 ```
 
 
@@ -345,7 +288,5 @@ In = 2.4e-06 [A/sqrt(Hz)]
 
 <style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
   <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Horowitz, Paul. 2015. <i>The Art of Electronics - Third Edition</i>. New York, NY, USA: Cambridge University Press.</div>
-  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Lafarga, Vicente. 2024. “Active Vibration Isolation System for Space Applications.” ULB.</div>
-  <div class="csl-entry"><a id="citeproc_bib_item_3"></a>Okyay, A. 2016. “Mechatronic Design, Dynamics, Controls, and Metrology of a Long-Stroke Linear Nano-Positioner.” University of Waterloo.</div>
-  <div class="csl-entry"><a id="citeproc_bib_item_4"></a>Schmidt, R. M., G. Schitter, and A. Rankers. 2020. <i>The Design of High Performance Mechatronics - Third Revised Edition</i>. Ios Press.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Schmidt, R. M., G. Schitter, and A. Rankers. 2020. <i>The Design of High Performance Mechatronics - Third Revised Edition</i>. Ios Press.</div>
 </div>