Update Content - 2020-09-09
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@ -38,9 +38,9 @@ Tags
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The piezoelectric stack can be represented as a capacitance.
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Let's take a capacitance driven by a voltage amplifier (Figure [1](#org4297943)).
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Let's take a capacitance driven by a voltage amplifier (Figure [1](#org81a4c8c)).
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<a id="org4297943"></a>
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<a id="org81a4c8c"></a>
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{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
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@ -60,7 +60,7 @@ Thus, for a specified maximum current \\(I\_\text{max}\\), the "power bandwidth"
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- Above \\(\omega\_{0, \text{max}}\\), the maximum current \\(I\_\text{max}\\) is reached and the maximum voltage that can be applied decreases with frequency:
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\\[ U\_\text{max} = \frac{I\_\text{max}}{\omega C} \\]
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The maximum voltage as a function of frequency is shown in Figure [2](#orgb578cd2).
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The maximum voltage as a function of frequency is shown in Figure [2](#orgc5c0812).
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```matlab
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Vpkp = 170; % [V]
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@ -74,7 +74,7 @@ C = 1e-6; % [F]
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56.172
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```
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<a id="orgb578cd2"></a>
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<a id="orgc5c0812"></a>
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{{< figure src="/ox-hugo/voltage_amplifier_max_V_piezo.png" caption="Figure 2: Maximum voltage as a function of the frequency for \\(C = 1 \mu F\\), \\(I\_\text{max} = 30mA\\) and \\(V\_{pkp} = 170 V\\)" >}}
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@ -86,19 +86,6 @@ If driven at \\(\Delta U = 100V\\), \\(C = 1 \mu F\\) and \\(I\_\text{max} = 1 A
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\\[ t\_c = \frac{100 \cdot 10^{-6}}{1} = 0.1 ms \\]
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### Bandwidth limitation (small signals) {#bandwidth-limitation--small-signals}
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This is takken from Chapter 14 of ([Fleming and Leang 2014](#orgd3659c0)).
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```matlab
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L = 250e-9; % Cable inductance [H]
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Cp = 10e-6; % Driving capacitance [F]
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Rs = 10; % Source impedance [Ohm]
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G = 1/(L*Cp)/(s^2 + Rs/L*s + 1/(L*Cp));
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```
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### Amplifiers for Low Voltage PZT {#amplifiers-for-low-voltage-pzt}
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Piezoelectric Stack Actuators are behaving like capacitor for the Amplifiers.
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@ -121,6 +108,27 @@ This can pose several problems:
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- the internal impedance of the amplifier may be large compared to the load impedance, and thus large voltage drop will occur
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### Noise {#noise}
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Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#org48e03fb)).
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Proper enclosures and cabling are necessary to protect the system from capacitive and inductive interferance.
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### Impedance of Voltage Amplifiers {#impedance-of-voltage-amplifiers}
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The **input** impedance of voltage amplifiers are generally set to \\(50 \Omega\\) to avoid any reflections of the signal.
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The **output** (or internal) impedance of voltage amplifier is generally wanted small in order to have a small voltage drop when large current are drawn.
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However, for stability reasons and to avoid overshoot (due to the internal negative feedback loop), this impedance can be chosen quite large.
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This is discussed in ([Spengen 2017](#org9c0a539)).
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## Bibliography {#bibliography}
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<a id="orgd3659c0"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
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<a id="orge4d11f6"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
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<a id="org9c0a539"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
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<a id="org48e03fb"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.
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