IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 5, OCTOBER 2006
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Measurement and Modeling Mutual Capacitance of Electrical Wiring and Humans William Buller, Member, IEEE, and Brian Wilson, Member, IEEE
Abstract—In a recent series of electric field sensing experiments, a theremin was used to measure the mutual capacitance between a human being and a length of electrical wiring. The instrument, based on the LM555 circuit, measures the deflections in capacitance due to the proximity of a human. The measurements are repeatable, and the difference in capacitance for a person at 0.5 m with a person at 1 m is consistent with the difference computed, assuming the human acts as a ground plane for the wiring. Much of the current literature in electric field sensing focuses on measures and models of mutual capacitance for humans interacting with plate conductors [J. R. Smith, Electric field imaging, Ph.D. dissertation, Mass. Inst. Technol., Cambridge, MA, 1999; N. Karlsson and J. O. Jarrhed, A capacitive sensor for the detection of humans in a robot cell, in Proc. IEEE IMTC Rec., May 18–20, 1993 pp. 164–166.], especially fingers near touch screens [D. Wiebe, A. Machynia, K. Mazur, and J. Epp, Human–computer interface device based on electric field sensing, Ph.D. dissertation, Univ. Manitoba, Winnipeg, MB, Canada, 2004]. The present investigation considers conducting wires to allow the development of portable rapidly deployable human proximity sensing systems that exploit existing electrical infrastructure in buildings. The experiment described here demonstrates that sensing with wires is possible at ranges on the order of a meter and provides evidence that modeling the person as a ground plane of finite extent provides a rough estimate of the change in mutual capacitance. Index Terms—Capacitance measurement, electric field effects, electric field measurement, man–machine systems, theremin.
I. I NTRODUCTION
A
S a musical instrument, the volume and pitch of a theremin [4] change, based on the proximity of the operator’s hands to the antennas of the instrument. The theremin concept is applied to proximity sensing by using a theremin circuit to measure the change in capacitance due to human proximity using electrical wiring as the instrument’s antenna. At 1 m from the wire, a human being causes a noticeable deflection in the capacitance measured along the wire. It was found that at 0.5 m, the mutual capacitance is increased by approximately 0.2 pF. Modeling the human being, the electrical wiring, and the ground plane as components in a three-body problem, the capacitance between the human and the wire can be computed by assuming that the person acts as an additional ground plane in the circuit. These assumptions yield a similar increase in mutual capacitance. Manuscript received June 20, 2005; revised June 13, 2006. The authors are with the Altarum Institute, Ann Arbor, MI 48105 USA (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/TIM.2006.880293
Electrical wiring was used as a theremin antenna with the idea that the theremin circuit could be connected at a central location in a building and nondiscriminately detect the presence of a human moving within the building. The experiments outlined in Section II are designed to demonstrate the concept of using a theremin to detect the motion of a human. Section III includes capacitance models that relate to the sensing problem. Section IV relates experimental results to those of the models shown in Section III.
II. E XPERIMENT S ETUP A. Theremin Thereminvision-II [5], which is a digital version of the theremin, was used to conduct the experiments. As shown in Fig. 1, Thereminvision-II is a heterodyne receiver comprised of two LM555-based oscillators. The reference oscillator operates at 1.8 MHz, and a variable oscillator is tuned near 1.7 MHz via a potentiometer that adjusts the RC time constant of the LM555 [6], which is used as a 50% duty cycle oscillator. The variable oscillator is connected to a 1-m length of 14-2 Romex electrical wire that acts as the theremin antenna. The difference signal of the two oscillators is outputted to a frequency divider set to divide the frequency by 4096. A BASIC stamp microcontroller is then used to count and store the pulse widths Tb associated with the beat frequency of the heterodyne receiver. An electrical wire connected to Thereminvision-II acts as the antenna, and its capacitance referenced to ground CW,G can be calculated from the pulse widths Tb as in (1), shown below. The derivation of this equation is based on the beat frequency between two LM555 timers. The relationship between CW,G and the proximity of a human is discussed in Section III, while the experimental results are shown in Section IV. The capacitance of the theremin circuit Cc was measured to account for parasitic capacitances on the board, i.e.,
CW,G = Cc
where Rr Rs Cc k
(kRr Rs Cc + Tb Rr − Tb Rs ) (−kRr Rs Cc + Tb Rs )
LM555 reference resistor; measured wire resistance; measured capacitance of theremin circuit; LM555constant = 2 log10 (2).
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Fig. 1. Circuit diagram from [5] showing that the heterodyne output of two LM555-based oscillators is measured by a counter. The frequency divider increases the maximum measurable frequency difference.
B. Configuration One meter of 14-2 Romex was pulled through two-by-four studs behind a sheet of drywall that is approximately 2 ft from the floor. The theremin is connected to the hot and neutral conductors in the cable with the ground wire left floating. In front of the wall, locations were labeled as in Fig. 2. Participants moved along the path from A to F, stopping at each location for 30 s. A laptop computer connected to Thereminvision-II through a BASIC stamp microcontroller collected data as described in Section II-A. Various courses and walking speeds were used for these trials; however, the results from other setups were similar to the results shown in Section IV. Fig. 2. Configuration of Romex and labeled locations for participants to stand. The arrows show the path participants followed.
III. M ODEL A. Three-Body Problem There are three bodies to consider as shown in Fig. 3, namely 1) the wire, 2) the human, and 3) the ground. There is an ambient capacitive coupling between the wire and ground CA . Parallel to this coupling is the coupling between the wire and the human CW,H and the human and ground in series CH,G ; therefore, the total capacitance between the wire and ground is CW,G = CA +
CW,H CH,G . CW,H + CH,G
(2)
In a stable environment, the capacitance between the wire and the ground is constant. The coupling between the human and the wire will depend on their overlap and distance. If we assume the overlap is constant, then as the distance between the human and the wire D changes, the capacitance will change as −2 dCW,H CW,H dCW,G = 1+ . (3) dD CH,G dD
Fig. 3.
Circuit diagram of three-body model.
The capacitance between the human and the ground has been estimated at 100–200 pF, but it may even be higher [7]. As the theremin only senses change in the capacitance between the wire and the ground CW,G , we cannot directly measure CH,G and CW,H . Assuming that CH,G is much greater than CW,H ,
BULLER AND WILSON: MEASUREMENT AND MODELING MUTUAL CAPACITANCE OF ELECTRICAL WIRING AND HUMANS
Fig. 4. Diagram showing the reasoning for restricting the capacitive coupling of the wire and a human to a wire of length z, which is approximately the width of a human being.
for D greater than 0.5 m, deflections measured on the theremin will primarily reflect the changes in the coupling between the wire and the human CW,H . This assumption is supported by the analytic solution in (5), which results in CW,H ≈ 1.7 pF, assuming a wire with a diameter of 1.6 mm at a distance of 0.5 m from a human, which is modeled as a 0.36-m-wide ground plane. The ground plane width in Fig. 4 is calculated using Ramanujan’s approximation for the circumference of an ellipse [8], assuming a human with a 34-in waist and with the ratio of the major axis and minor axis of the ellipse being 2 : 1. The interest in detection at ranges of 0.5–1 m is to satisfy the intended application for proximity sensing of people in buildings using the existing building infrastructure and a centrally located theremin circuit. B. Capacitance of a Wire Above a Ground Plane The 14-gauge wire connected to the theremin is modeled as a conducting cylinder with radius of 0.8 mm. The human is modeled as a conducting plane. The equation for the capacitance of a transmission line over a ground plane is computed here by the method of images, replacing the ground plane at D with an image wire at 2D. The equation for the capacitance between two wires at this distance, which is derived in [9], is given as πε0 πε0 dC = = −1 −1 dz cosh (2D/2a) cosh (D/a)
(4)
where ε is the permittivity of free space, z is the length of the wire, and a is the radius. IV. R ESULTS A. Empirical Three participants followed the course, stopping at each point for 30 s. Participant 1 is 6 ft 1 in and 200 lb. Participant 2 is 5 ft 10 in and 170 lb. Participant 3 is 5 ft 9 in and 190 lb. An example of annotated data is shown in Fig. 5. The example data show that the proximity of the person records a noticeable deflection
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Fig. 5. Annotated plot from the collection of data for Participant 3 following the course depicted in Fig. 2. The vertical lines specify when the participant was requested to move to the position identified by the letter. An increase in capacitance is clearly visible as Participant 3 approaches the wire. The difference in mutual capacitance when Participant 3 is at Positions C and D (0.5 m from the wire) and at Positions B and E (1 m from the wire) is ∼0.2 pF. TABLE I MEASURED CHANGE IN MUTUAL CAPACITANCE (IN FEMTOFARADS) FOR H UMAN P ARTICIPANTS M OVING F ROM 1 TO 0.5 m A WAY FROM 14-2 ROMEX CABLE. VALUES ARE RECORDED FOR EACH PARTICIPANT ALONG WITH ONE STANDARD DEVIATION
at 1 m (positions B and E) and at 0.5 m (positions C and D). Beyond 2 m, the deflections are not sensible. We have conducted many experiments with similar results. These experiments involved altering the course, speed of travel, and stance (i.e., standing on one leg) of the participant. The example in Fig. 5 was chosen as a representative sample of the experiments in part because the background capacitance shows no significant drift. The mean and standard deviation of the differences in mutual capacitance at 1 and 0.5 m for all three participants are recorded in Table I in femtofarads. The standard deviation of the background noise was used for the values shown in Table I, and it represents the sensitivity of the hardware used for our experiments. B. Analytic Solution Integrating (4) over a finite length z in (5) provides a firstorder approximation for the mutual capacitance between one wire and a human, i.e., CW,H =
πε0 z cosh−1 (D/a)
where the permittivity constant ε0 is 8.85 pF/m.
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Using the width of a person as an estimate for the length of the wire z contributing to CW,H to be 0.36 m, the difference in capacitance computed at 0.5 and 1 m from the Romex is CW,H (0.5 m) − CW,H (1 m) =
πε0 (0.36) πε0 (0.36) − ≈ 150 fF. (6) cosh (0.5/0.0008) cosh−1 (1/0.0008) −1
This estimate, which is intended as an order of magnitude estimate, is in good agreement with the values measured by the theremin. Further work in this area is required to support the simple model proposed above. The primary result of this paper is to empirically establish the capacitive coupling between a human being and the typical electrical wiring at distances appropriate for a proximity sensor and to provide a first-order model. V. C ONCLUSION The measurements and calculations here are results of ongoing experiments to develop a rapidly deployable centralized human proximity sensing system in buildings with existing electrical infrastructure. As part of this inquiry, the authors have measured the coupling of adult humans with Romex cable installed through a wood frame wall behind a plaster board. The measurements demonstrate the mutual capacitance between a human and standard electrical wiring to be sufficient for proximity detection at distances on the order of 1 m. The difference in this coupling at distances of 0.5 and 1 m is well within an order of magnitude of our calculation made on the model that a person acts as a finite ground plane. Continuing research is providing promising results that a building scale system is feasible. ACKNOWLEDGMENT The authors would like to thank C. Roussi for the original concept of this work, N. Subotic, P. Jensen, J. Ruiter, and J. Burns for their efforts, and the reviewers who greatly improve this paper.
R EFERENCES [1] J. R. Smith, “Electric field imaging,” Ph.D. dissertation, Mass. Inst. Technol., Cambridge, MA, 1999. [2] N. Karlsson and J. O. Jarrhed, “A capacitive sensor for the detection of humans in a robot cell,” in Proc. IEEE IMTC Rec., May 18–20, 1993, pp. 164–166. [3] D. Wiebe, A. Machynia, K. Mazur, and J. Epp, “Human-computer interface device based on electric field sensing,” Ph.D. dissertation, Univ. Manitoba, Winnipeg, MB, Canada, 2004. [4] A. Glinsky, Theremin: Ether Music and Espionage, Urbana and Chicago. Urbana, IL: Univ. Illinois Press, 2000, pp. 253–254. [5] T. Fritz, Thereminvision-II. [Online document] Accessed Jul. 17, 2006. [Online]. Available: http://thereminvision.com/version-2/TV-II-index.html [6] National Semiconductor Technical Staff, LMC555 CMOS Timer Data Sheet, National Semiconductor, pp. 1–10, Mar. 2002. [Online]. Available: http://cache.national.com/ds/LM/LMC555.pdf [7] N. Jonassen, “Human body capacitance: Static or dynamic concept?,” in Proc. [ESD] Electr. Overstress/Electrost. Disch. Symp., Oct. 6–8, 1998, pp. 111–117. [8] S. Ramanujan, “Ramanujan’s collected works,” Ellipse, 1962, Chelsea, NY. Wikipedia, the Free Encyclopedia. [Online]. Available: http://en. wikipedia.org/wiki/Ellipse [9] D. De Wolf, Essentials of Electromagnetics for Engineering. Cambridge, U.K.: Cambridge Univ. Press, 2001.
William Buller (M’00) received the B.A. degree in physics from Albion College, Albion, MI, and the M.S. degree in engineering physics from the University of Virginia, Charlottesville. He was with the Technology Service Corporation, where he led research efforts on inference for automated target recognition for naval radar systems. In 2004, he joined the Environmental and Emerging Technologies Division (formerly ERIM), Altarum Institute, Ann Arbor, MI. He is currently investigating multistatic radar concepts, EM field sensing, and interferometry.
Brian Wilson (M’04) received the B.S.E. degree in electrical engineering, the M.S.E. degree in electrical engineering, and the M.S. degree in biomedical engineering from the University of Michigan, Ann Arbor. In 2004, he joined the Altarum Institute, Ann Arbor, as an Analyst for the Environmental and Emerging Technologies Division (formerly ERIM).
