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