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sensors:linear_variable_differential_transformer [2021/03/22 21:19] – [Signal Conditioning] greg.sikorasensors:linear_variable_differential_transformer [2021/03/24 21:03] (current) – [External links & references] greg.sikora
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 One of the secondary windings, being wound in opposite direction to the other two inductors, will output the excitation signal in the opposite phase. This is used in order to obtain a differential voltage indicating the direction of the displacement: the outputs of the secondary windings are rectified and summed to produce a voltage that varies linearly between the +/- the maximum displacement with the centre position being at zero volts. One of the secondary windings, being wound in opposite direction to the other two inductors, will output the excitation signal in the opposite phase. This is used in order to obtain a differential voltage indicating the direction of the displacement: the outputs of the secondary windings are rectified and summed to produce a voltage that varies linearly between the +/- the maximum displacement with the centre position being at zero volts.
  
-The simplest forms of demodulation involve some form of diode rectification, while more complex structures involve synchronous demodulation. In either case, the secondary coils' output is processed through low-pass filtering to remove AC components and leave a DC signal proportional to the displacement. When measuring absolute voltage values, one must account for offset errors and drifts and other measurement inaccuracies. Hence, nearly all LVDT circuitry today uses a **ratiometric design** (or "Sum of Secondary Feedback" method for non-uC circuits). It is a common and well-known technique for eliminating absolute errors using ratios between values. Ratiometric methods are applied to eliminate changes due to the excitation voltage shifts when measuring LVDT signals and compensates for any drifts or other LVDT construction inaccuracies. Such a process requires more complicated circuitry than a non-ratiometric design (e.g., synchronous detection) - it provides significant benefits. Additionally, it is only valid if the core is kept sufficiently within both coils and the sum of secondary coils' signals remains relatively constant (Nyce2004). Nowadays, the difference in circuitry is not problematic due to the advances in IC design and microcontrollers. +The simplest methods of demodulation involve some form of diode rectification, while more complex structures involve synchronous demodulation. In either case, the secondary coils' output is processed through low-pass filtering to remove AC components and leave a DC signal proportional to the displacement. When measuring absolute voltage values, one must account for offset errors and drifts and other measurement inaccuracies. Hence, nearly all LVDT circuitry today uses a **ratiometric design** (or "Sum of Secondary Feedback" method for non-uC circuits). It is a common and well-known technique for eliminating absolute errors using ratios between values. Ratiometric methods are applied to eliminate changes due to the excitation voltage shifts when measuring LVDT signals and compensates for any drifts or other LVDT construction inaccuracies. Such a process requires more complicated circuitry than a non-ratiometric design (e.g., synchronous detection) - but it provides significant benefits. Additionally, it is only valid if the core is kept sufficiently within both coils and the sum of secondary coils' signals remains relatively constant (Nyce2004). Nowadays, the difference in circuitry is not problematic due to the advances in IC design and microcontrollers. 
  
 A simplified ratiometric signal conditioning (Szczyrbak1997): A simplified ratiometric signal conditioning (Szczyrbak1997):
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 {{ :sensors:vemuri.png?nolink&600 |}} {{ :sensors:vemuri.png?nolink&600 |}}
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-Below, a __simplified__ mathematical model of the LVDT demodulation (hover over the image for caption): +Below, a __simplified__ mathematical simulation of the LVDT (MaxMSP) demodulation: 
-{{ :sensors:matlab1.png?nolink&400 |Simulation of the core displacement (3 sec., 0.5 - null position, the blue line represents core displacement)}}+{{ youtube>4fGsUOM2kjI?large }} 
 +----
  
-{{ :sensors:matlab2.png?nolink&400 |Secondary coils excited with a sinusoidal signal (Fe = 10 Hz, for the purpose of visualization)}}+==== Signal Conditioning (Other) ==== 
 +Another interesting approach for demodulation consists of the low-cost elements and is based on the sample & hold circuitry instead of the traditional rectification and low-pass. Such an approach provides better speed performance (integration every half-cycle of excitation frequency) of the LVDT and reduces circuit complexity. 
 +{{ :sensors:sah1.jpg?nolink&700 |Petchmaneelumka2017}}
  
-{{ :undefined:matlab3.jpg?nolink&400 |Full-wave rectification of the signals at secondary coils}} +In (Petchmaneelumka2017) "(…) simple circuit technique to realize the LVDT signal to DC voltage converter is introduced. The technique is based on the ratio of sum and difference of the signals from two secondary windings. The proposed scheme comprises an operational amplifier (opamp) and operational transconductance amplifier (OTA) as an active circuit building block. The sum of two secondary winding signals is provided for the reference signal to generate the control signal for the SHC. The control signal for the SHC is obtained by the peak-amplitude finder (…)". Other techniques introduced by the same author propose even simpler, yet effective, LVDT demodulation.
- +
-{{ :sensors:matlab4.png?nolink&400 |Low-pass filtering}} +
- +
-{{ :sensors:matlab5.png?nolink&400 |Fully demodulated signal (difference over sum)}} +
- +
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-A similar mathematical simulation (MaxMSP) of the LVDT with demodulation: +The time-series below illustrate the signal path progression, from primary coil excitation signal (V1) and voltage on the sum of secondary coils (Vd), through peak detection (Vc) to trigger sample&hold circuit, to the final output Vo proportional to the core displacement.  
-{{ youtube>AudtIkBpXbo }}+{{ :sensors:sah2.jpg?nolink&400 |Petchmaneelumka2017}}
  
  
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   * (Hoadley1936) George B Hoadley, “Telemetric System”. US Patent Application #2196809, March 17th 1936 (Patented on April 9th 1940).   * (Hoadley1936) George B Hoadley, “Telemetric System”. US Patent Application #2196809, March 17th 1936 (Patented on April 9th 1940).
   * (Powell2009) Mike Powell, //[[http://www.mikesflightdeck.com/lvdt_circuitry.htm|Mike’s Flight Deck]]//   * (Powell2009) Mike Powell, //[[http://www.mikesflightdeck.com/lvdt_circuitry.htm|Mike’s Flight Deck]]//
 +  * [[http://nliebeaux.free.fr/ressources/signal.pdf|(Szczyrbak1997)]] Szczyrbak, J. "LVDT Signal Conditioning Techniques", 1997
 +  * [[https://www.ti.com/lit/an/slyt704/slyt704.pdf?ts=1616609560481&ref_url=https%253A%252F%252Fwww.google.com%252F|(Vemuri2017)]] Vemuri, A. & Torres, H. "Signal-to-noise ratio of an LVDT amplitude demodulator", Analog Applications Journal, 2017
 +  * [[https://dl.acm.org/doi/10.1145/3057039.3057103|(Petchmaneelumka2017)]] Petchmaneelumka, W., Songsuwankit, K. & Riewruja, V. "Simple LVDT Signal to DC Converter", 2017
   * eFunda, 2005, //[[http://www.efunda.com/designstandards/sensors/lvdt/lvdt_theory.cfm|Theory of linear variable differential transformer (LVDT).]]//     * eFunda, 2005, //[[http://www.efunda.com/designstandards/sensors/lvdt/lvdt_theory.cfm|Theory of linear variable differential transformer (LVDT).]]//  
   * RDP Group, 2002, //[[http://www.rdpe.com/displacement/lvdt/lvdt-principles.htm|LVDT principle of operation.]]//   * RDP Group, 2002, //[[http://www.rdpe.com/displacement/lvdt/lvdt-principles.htm|LVDT principle of operation.]]//