Added Eliska's parameters

cad0d335 · Pascal Engeler · 16952589 · cad0d335
Commit cad0d335 authored 5 years ago by Pascal Engeler
--- a/parameter_calculation/Untitled.ipynb
+++ b/parameter_calculation/Untitled.ipynb
@@ -241,6 +241,67 @@
    "Note that we choose coordinates where drums from both, sublattice A and B, are displaced in positive direction when they move closer to their respective driving electrode."
   ]
  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Eliska parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 168,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = 1.\n",
+    "f = 25000.\n",
+    "m = 2328*(1e-6)*(np.pi*((250e-6)**2))\n",
+    "k_loc = m*((2.0*np.pi*f)**2)\n",
+    "k_coup = k_loc*0.2\n",
+    "k_base = k_coup*0.1\n",
+    "Q = 30000.\n",
+    "c = (2.0*np.pi*f/Q)\n",
+    "l0 = 5.\n",
+    "delta0 = 1.\n",
+    "alpha = 1."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 169,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "m: 4.571017310973148e-10\n",
+      "localStiffness: 11.278533142459056\n",
+      "k0_A: 27388152213.022964\n",
+      "k0_B: 21959869792.42382\n",
+      "k1: 493480220.0544679\n",
+      "k2: 2467401100.2723393\n",
+      "c: 5.235987755982988\n",
+      "l0: 5.0\n",
+      "delta0: 1.0\n",
+      "alpha: 1.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"m: {m}\")\n",
+    "print(f\"localStiffness: {k_loc}\")\n",
+    "print(f\"k0_A: {k_loc/m+1.1*0.5*k_coup/m}\")\n",
+    "print(f\"k0_B: {k_loc/m-1.1*0.5*k_coup/m}\")\n",
+    "print(f\"k1: {k_base/m}\")\n",
+    "print(f\"k2: {k_coup*0.5/m}\")\n",
+    "print(f\"c: {c}\")\n",
+    "print(f\"l0: {l0}\")\n",
+    "print(f\"delta0: {delta0}\")\n",
+    "print(f\"alpha: {alpha}\")"
+   ]
+  },
  {
   "cell_type": "code",
   "execution_count": null,

 %% Cell type:code id: tags:

 ``` python
 import numpy as np
 import matplotlib.pyplot as plt
 ```

 %% Cell type:markdown id: tags:

 # Units

 The units that suit the situation are

 Mass: ug

 Voltage: uV

 Current: nA

 Capacitance: mF

 Charge: nC

 Time: ms

 Frequency: kHz

 Length: um

 %% Cell type:code id: tags:

 ``` python
 #Drum parameters:
 drum_diameter = 1000. #um
 drum_thickness = 0.3 #um
 electrode_thickness = 0.05 #um
 electrode_area = 200.*200. #um^2
 drum_gap = 1. #um
 drum_resonance = 10. #kHz
 drum_Q = 10000. #no units
 ```

 %% Cell type:code id: tags:

 ``` python
 #Physical constants
 rho_si3n4 = 3.44e-6 #ug/um^3
 rho_au = 1.93e-5 #ug/um^3
 coulomb_k = 9.0e12 #um/mF
 permittivity = 8.85e-15 #mF/um or nN/(mV)^2
 ```

 %% Cell type:code id: tags:

 ``` python
 #Drum mass
 m_si3n4 = (0.5*drum_diameter)**2*3.141592653589793*drum_thickness*rho_si3n4
 m_au = 4.*electrode_area*electrode_thickness*rho_au
 m = m_si3n4 + m_au
 print(f'Si3N4 Mass: {m_si3n4}')
 print(f'Au Mass: {m_au}')
 print(f'Drum Mass: {m}')
 ```

 %% Output

    Si3N4 Mass: 0.8105309046261666
    Au Mass: 0.1544
    Drum Mass: 0.9649309046261666

 %% Cell type:code id: tags:

 ``` python
 #Drum capacitance
 capacitance = permittivity*electrode_area/drum_gap #nC/uV
 print(f'Capacitance: {capacitance} nC/uV')
 ```

 %% Output

    Capacitance: 3.54e-10 nC/uV

 %% Cell type:code id: tags:

 ``` python
 #Electrode charge
 def charge(volt):
    return capacitance * volt*1e6
 ```

 %% Cell type:code id: tags:

 ``` python
 print(f'Charge at 5V: {charge(5.)} pC')
 ```

 %% Output

    Charge at 5V: 0.00177 pC

 %% Cell type:code id: tags:

 ``` python
 def force(volts):
    nanocouls = charge(volts)
    return coulomb_k * nanocouls*(-nanocouls) / drum_gap**2
 ```

 %% Cell type:code id: tags:

 ``` python
 print(f'Force at {drum_gap} um and 5 V: {force(5.)} nN = {force(5.)*1e-6} mN')
 ```

 %% Output

    Force at 1.0 um and 5 V: -28196100.0 nN = -28.196099999999998 mN

 %% Cell type:code id: tags:

 ``` python
 #Damping coefficient
 c = 2.*3.141592653589793*drum_resonance / drum_Q
 ```

 %% Cell type:code id: tags:

 ``` python
 #Print relevant parameters
 print(f"Gap: {drum_gap} um")
 print(f"1/Gap^2: {1./drum_gap**2} um^2")
 print(f"2/Gap^3: {2./drum_gap**3} um^3")
 print(f"Stiffness k: {(2 * np.pi * drum_resonance)**2 * m} ug/ms^2")
 print(f"Capacitance: {capacitance:.8E} nC/uV")
 print(f"Coulomb_k * Capacitance^2 / m: {coulomb_k*capacitance**2/m:.8E} um/mF")
 print(f"Prefactor k_pf:  {permittivity * electrode_area / (4. * m * drum_gap**2):.8E} mFum/ug")
 print(f"Drum Mass: {m:.8E} ug")
 print(f"[F] = nN")
 print(f"Damping c: {c:.8E} kHz")
 print(f"w^2: {(2.*3.141592653589793*drum_resonance)**2/m:.8E} kHz^2")
 ```

 %% Output

    Gap: 1.0 um
    1/Gap^2: 1.0 um^2
    2/Gap^3: 2.0 um^3
    Stiffness k: 3809.39452121822 ug/ms^2
    Capacitance: 3.54000000E-10 nC/uV
    Coulomb_k * Capacitance^2 / m: 1.16883395E-06 um/mF
    Prefactor k_pf:  9.17164116E-11 mFum/ug
    Drum Mass: 9.64930905E-01 ug
    [F] = nN
    Damping c: 6.28318531E-03 kHz
    w^2: 4.09132068E+03 kHz^2

 %% Cell type:markdown id: tags:

 # Force per unit mass

 The force per unit mass is now

 $\text{F} / \text{m} = \text{Hooke} + \text{Damping} + \text{Drive} + \text{Coupling}$,

 with

 $\text{Hooke} = - \omega^2 \, x,$

 $\text{Damping} = - c \, \dot{x},$

 $\text{Drive} = k_{\text{pf}} \, V^2 \, (1. + \frac{x}{\text{gap}}),$

 $\text{Coupling} = \sum_i k_{\text{pf}} \, t_i^2 \, (1. + \frac{x + x_i}{\text{gap}}),$

 where

 $k_\text{pf} = \frac{\varepsilon_0\,A}{4\,m\,\text{gap}^2}$

 and V, t_i are the driving voltage and the coupling electrode i voltage.

 Note that we choose coordinates where drums from both, sublattice A and B, are displaced in positive direction when they move closer to their respective driving electrode.

+%% Cell type:markdown id: tags:
+
+# Eliska parameters
+
+%% Cell type:code id: tags:
+
+``` python
+a = 1.
+f = 25000.
+m = 2328*(1e-6)*(np.pi*((250e-6)**2))
+k_loc = m*((2.0*np.pi*f)**2)
+k_coup = k_loc*0.2
+k_base = k_coup*0.1
+Q = 30000.
+c = (2.0*np.pi*f/Q)
+l0 = 5.
+delta0 = 1.
+alpha = 1.
+```
+
+%% Cell type:code id: tags:
+
+``` python
+print(f"m: {m}")
+print(f"localStiffness: {k_loc}")
+print(f"k0_A: {k_loc/m+1.1*0.5*k_coup/m}")
+print(f"k0_B: {k_loc/m-1.1*0.5*k_coup/m}")
+print(f"k1: {k_base/m}")
+print(f"k2: {k_coup*0.5/m}")
+print(f"c: {c}")
+print(f"l0: {l0}")
+print(f"delta0: {delta0}")
+print(f"alpha: {alpha}")
+```
+
+%% Output
+
+    m: 4.571017310973148e-10
+    localStiffness: 11.278533142459056
+    k0_A: 27388152213.022964
+    k0_B: 21959869792.42382
+    k1: 493480220.0544679
+    k2: 2467401100.2723393
+    c: 5.235987755982988
+    l0: 5.0
+    delta0: 1.0
+    alpha: 1.0
+
 %% Cell type:code id: tags:

 ``` python
 ```