diff --git a/content/zettels/voltage_amplifier.md b/content/zettels/voltage_amplifier.md index 4671f4d..f715c0a 100644 --- a/content/zettels/voltage_amplifier.md +++ b/content/zettels/voltage_amplifier.md @@ -38,9 +38,9 @@ Tags 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)). - + {{< 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: \\[ 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 Vpkp = 170; % [V] @@ -74,7 +74,7 @@ C = 1e-6; % [F] 56.172 ``` - + {{< 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 \\] -### 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} 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 +### 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} -Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. . +Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. . + +Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems. + +———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.