Square magnetic loops are very useful troubleshooting and noise investigation tools for electronics. They are adequate for coupling signals into a PCB or measuring noise in a circuit. This article describes the construction and characteristics of unshielded and shielded magnetic loops as well as comparing them.
Often the simplest of tools can be used to successfully track down a problem in a circuit. Magnetic loops (magnetic near field probes) are very useful troubleshooting and noise investigations tools for electronics both in emissions and susceptibility subjects -. They can be found from many vendors - both shielded and unshielded usually in round forms.
Square loops are very useful for making measurements of circuit voltage and current while either square or round loops are suitable for measuring magnetic fields in free space .
A magnetic field probe built from a short piece of wire is very useful for making Mdi/dt voltage measurements in circuits, to measure the relative phase or time delay between two signals, to locate a noise source or to inject signals into a path on a circuit board. The application of this technique to impulsive signals has been made practical with the advent of relatively inexpensive, portable, and fast digitizing scopes.
Occasionally, a shielded loop is called for and usually shielded loops are made from semi-rigid coaxial cable.
In this article, square unshielded wire loops are compared to shielded solutions including simple techniques to build them in your lab. Some examples are included to show that unshielded loops often work as well as shielded loops in some applications, especially for injecting signals into circuits.
Unshielded Magnetic Loops
Figure 1 shows the construction of a paper clip probe. Two minutes, some heat shrink tubing, and a pair of needle nose pliers are all that is needed. A BNC barrel adapter makes a convenient mounting for the loop. The result is a square shape, covered with insulation, forming an unshielded magnetic loop probe.
Figure 1: Magnetic field probe build from a paper clip.
A conductor carrying a current, i, will have a voltage drop across it given by:
e1 = Ldi/dt + Ri (1)
where L is the inductance per unit length of the conductor; R is the resistance per unit length and e1 is the voltage drop per unit length. The unit length will be small compared to a wavelength at the highest frequency of interest. That means the conductor is electrically short.
At frequencies above a few hundreds of kHz, the resistive component becomes negligible and (1) simplifies to just:
e1 = Ldi/dt (2)
A conductor nearby the current carrying conductor, such as a side of the square loop above, will pick up an open circuit voltage of:
e2 = Mdi/dt (3)
where M is the mutual inductance between the current carrying wire and the nearby wire per unit length.
Since L and M are constants, then e1 and e2 are only different by a constant. M must be smaller than L for two parallel wires (due to the magnetic flux that flows between the wires instead of enclosing both), so e1 is a lower bound estimate for the magnitude of e2 and has the same wave shape.
Using that principle, a simple square loop, such as the one above, can be used to estimate the voltage drop across conductors. When the probe is held up to a conductor carrying high frequency current, the probe’s open circuit output voltage is a lower bound for the voltage between the corners of the probe along the current carrying conductor as measured by the magnetic field captured in the area of the loop.
The probe should be connected to an oscilloscope or spectrum analyzer using a coaxial cable terminated in its characteristic impedance. This resistive load on the loop in combination with the self inductance of the loop forms a low pass filter on the probe output. For a loop with sides of 1 cm, this corner frequency will be between 200 and 300 MHz.
Possible uses are estimating the drop across bonding wires and lead frames of integrated circuits  or measuring noise effects on a printed wiring board .
An Easy to Build Shielded Magnetic Loop Probe
Occasionally, a shielded loop is called for and usually shielded loops are made from coaxial cable. The loop is formed by making a square from the coax with a gap and soldering inner conductor to shield in point (A) as in Figure 2.
Figure 2: Square loop from a coax cable unshielded (left) and shielded (right).
Figure 3 shows the construction steps for quickly and simply making a shielded magnetic loop in the lab.
Figure 3: Building a shielded loop.
Step 1: Take a piece of stiff copper wire or rod (16 gauge is best for fitting in BNC connector). The wire is covered with heat shrink tubing and then copper tape is wound around the heat shrink tubing so that it is covered with three layers of tape. In that way, when the wire is bent to form a square loop, the outermost layer may crack slightly. Since the crack is only on the outside of the bend and it is small, it does not pose much of a problem because the gap will be closed by the underlying layers.
The characteristic impedance of the coax formed by the foil and stiff wire is probably not 50 Ohms like the feed cable likely is. But, it does not matter much since the two parasitic transmission lines formed by the two halves of the loop and their shields are un-terminated at the gap in any event.
Step 2: Put a second layer of heat shrink tubing over the assembly.
Step 3: The loop is then bent and one end inserted into a BNC connector. Both the other end of the wire and copper tape are soldered to the side of the BNC connector.
Step 4: Next, the end of the BNC connector and two ends of the loop are covered in copper tape which is soldered to the copper foil of the loop. The added copper tape may also be soldered to the BNC connector as well.
Step 5: Finally, the assembly is covered with heat shrink tubing to make the final product. The position of the gap is very important to the performance of the shield. A shielded loop that is not symmetric (e.g. gap at base of loop) will be somewhat sensitive to E fields. E field induces current in shield so there is voltage drop across shield that will be induced into center conductor loop .
Better shielding effectiveness is obtained if the gap is located in the middle of the loop as shown in Figure 4. In that way, electric field symmetry is obtained.
Figure 4: Square loop from a coax cable unshielded (left) and shielded (right).
The loop is formed by making a square from the coax with a gap placed symmetrically in the middle of the loop as in Figure 4. The center wire is connected again to shield in point (A).
The loop’s shielding may be tested as described in  by applying an electric field source to the loop. The loop should be least sensitive over the gap with the maximum sensitivity just off the gap in either direction. The sensitivity should gradually fall off as the electric field source is moved toward the side of the loop (at the BNC connector) opposite the gap.
Square Shielded Loop with Semi-rigid Coax
One can minimize the work required to build a shielded loop by buying a short length of small semi-rigid coaxial cable with SMA connectors already mounted on each end . The assembly can be cut in half to make two shielded loops saving the trouble of mounting the connectors on the semi-rigid cable.
Use a small diameter semi-rigid cable as the smaller the semi-rigid coax diameter, the better coupling between the center conductor of the coax and the adjacent circuit.
For our purposes, one can think of the loop as starting with a straight length of semi-rigid coax of small diameter with an SMA connector on one end and shorting the center conductor to the shield with solder at the other end. Then the loop is bent around to form a square (being careful not to bend the coax too sharply at the corners) and the solder shorted end is soldered back on the coax so as to form a square symmetric loop. A small gap is made in the shield in the middle of the side opposite the feed line. Figure 5 shows a square shielded loop built  into a plastic housing which has been split to show the loop inside.
Figure 5: Cutaway View of a Square Shielded Loop
Shielding against electric fields is best achieved if the field is symmetric around a line from the solder junction to the gap in the shield, a condition that is met when a shielded loop is used to measure a field much further from a source than the size of the source itself.
To help ensure electric field symmetry when the loop is used on the surface of a circuit board in the near field, the gapped side should be held against the board with the loop itself perpendicular to the board. And therein lies the main reason for using a square loop, most circuit boards are flat and one side of the loop can be held directly against a circuit board resulting in better coupling to the circuit than a round loop of the same size would give.
The performance of a loop constructed in the previous section (Figure 3) should compare favorably with one made from semi-rigid coaxial cable up to the first resonance of the loop. The first resonance occurs at the frequency where the circumference of the loop is one half wavelength. At this frequency, the parasitic transmission lines formed by the two shields and the underlying stiff wire are one quarter wavelength un-terminated stubs.
Square shielded loops can be used both to measure many kinds of signals and to inject small RF signals (~0 dBm) into circuits. Some of the techniques involve coupling high voltage/current short pulses into a circuit. For that application shielded loops made from small semi-rigid coax are not a good option for this purpose because of possible voltage breakdown in the coax and even heating under some conditions. For large pulses, use unshielded stiff wire loops.
Parasitic Coupling Between Unshielded Wire Loops
Unshielded wire loops are inexpensive and easy to build but capacitive (electric field) coupling has always been a concern when using these simple loops. Coupling between unshielded wire loops is investigated, included parasitic capacitive coupling.
Figure 6 shows an overall view of the test setup comprised of a pair of square wire unshielded loops connected to an Agilent N1996A spectrum analyzer set up to perform a two port insertion loss measurement. The two loops are about one inch, a few cm, on a side and they are positioned end-to-end.
Figure 6: Measuring loop to loop coupling for a pair of square shielded loops (end-to-end) in reversed direction.
In Figure 6, the loops are reversed in position, that is the + side of one loop (center conductor of BNC) is opposite the – of the other loop (ground side of BNC). This will be referred to as the “reversed” direction. By inverting one of the loops the “normal” direction is obtained (+ side to + side of the loops). Data is presented for both directions.
If only magnetic field coupling existed between the loops, the change resulting when one of the loops is reversed would be a 180 degree phase shift in the output, which would not change the spectrum analyzer plot.
If significant capacitive coupling existed between the loops, the output of the receiving loop would be the combination of the inductive and capacitive components. Since the phase of the inductive component is reversed when one loop is reversed but the phase of the capacitive component is not, the spectrum analyzer plot will be different.
In other words, capacitive coupling between the loops would cause the normal and reversed positions of the loops to yield different responses.
Figure 7(a) and 7(b) show the loop-to-loop transmission from 10 MHz to 1 GHz for the reversed case and normal cases of the two loops. No resonance is found, with the frequency response being relatively flat by comparison. The differences are about 6 dB maximum at a few frequencies and the traces are not as smooth as the shielded loops. However, the “lumps” in the frequency response are only a few dB in peak amplitude. The relatively flat frequency response in Figure 7 is indicative that simple wire loops may be useful for injecting signals into circuit board paths and cables by inductive coupling. Using loops for this purpose will be covered in parts VII and VIII.
Figure 7: Response end-to-end loops reversed and normal directions.
Figure 8 shows the overview of a related case where the loops are overlapped to insure maximum coupling. Notice that the loops are arranged in the normal position as opposed to reversed in Figure 6, that is the sides of the loops connected to the BNC center pin (or shield connection) are both on the same side.
Figure 8: Measuring loop to loop coupling (loops overlapped).
Figures 9(a) and 9(b) (page 80) show the coupling from 10 MHz to 1 GHz for the setups in both the reversed and normal orientations. The difference between the two traces is only a few dB, and without shielding!
Figure 9: Response of overlapped loops reversed and normal directions.
Frequency response plots of the coupling between small simple wire loops are reasonably flat.
Parasitic coupling electric field Shielding in square shielded magnetic loops.
We have introduced before that shielded magnetic loops are used to reduce electric field coupling to the loop and square magnetic loops are useful for coupling signals into a PCB or measuring noise in a circuit. However, significant electric field coupling can still occur with shielded loops. One case of electric field coupling between a pair of shielded loops is presented which results in a significant resonance between the shielded loops. Such a resonance can cause errors in signal injection used for troubleshooting circuits.
Figure 10 shows an overall view of the test comprised of a pair of square shielded loops connected to an Agilent N1996A spectrum analyzer with a tracking generator which is set up to perform a two port insertion loss measurement. The two loops are positioned end-to-end and held in place with paper tape on the back of the loops. The semi-rigid coax used to form the loops is encased in plastic as explained in Figure 5.
Figure 10: Measuring loop to loop coupling for a pair of square shielded loops and close-up of loops for coupling measurement.
Figure 11 shows the resulting plot of insertion loss (un-normalized) between 10 MHz and 1 GHz. Notice the significant dip of around 30 dB at about 394 MHz.
Figure 11: Plot of loop to loop coupling showing resonance.
This resonance can be explained with reference to Figure 12.
Figure 12: Circuit of parasitic resonance
The capacitance Co between the shield segments shown in Figure 12, form a resonant circuit with the inductance of the two loops. The current path for the resonance is shown by red arrows. The loops used for this test are one inch on a side, so the effective loop for the resonant circuit is approximately two inches by one inch.
The theoretical calculation of inductance  gives a value of about 125 nH for such a loop assuming a wire (shield) radius of 10 mils. The resonant frequency of 394 MHz then yields a capacitance of about 1 pF for the total capacitance in the tuned circuit of Figure 12. Adding ferrite to the coax cables feeding the loops did not change the characteristics of Figure 11 so the current loop of Figure 12 is the controlling feature.
Current flowing in the center conductor of the driven loop generates inductive voltage drop (Ldi/dt) around the loop. A shielded cable is nearly an ideal transformer, so the voltage drop on the center conductor under each of the two shield segments is magnetically coupled into the shield segments as Mdi/dt. The mutual inductance, M, between the center conductor and the shield, is the inductance of the shield itself.
This driving voltage on the two shield segments causes current to flow around the four shield segments coupled by the parasitic capacitance between the loop shields as shown in Figure 12 thus driving the resonant circuit. In this discussion, we are treating the circuit as composed of lumped elements since each segment and the loops themselves are small compared to a wavelength at 400 MHz.
If a resonance caused by the current path of Figure 12 is the reason for the dip in plot in Figure 11, then moving the loops apart should increase the resonant frequency. This would happen because the capacitance Co between the loops is reduced. Figure 13 shows the test setup modified to space the loops one cm apart. The two loops are taped to a plastic ruler to maintain the spacing during the measurement as shown in the close-up detail.
Figure 13: Measuring loop to loop coupling for a pair of square shielded loops at one cm spacing including a close-up.
The resulting two port insertion loss plot is shown in Figure 14. Note that the resonant dip has moved to about 495 MHz. This would represent a significant drop in capacitance on the order of 40%. As the loops are moved further apart, L gets slightly larger but C gets much smaller. As the distance is increased, the capacitance between all parts of the loops begins to contribute an increasing portion of the capacitance between the loops complicating the picture somewhat. One would not expect the capacitance to decrease as much as just that of the facing sides as the loops are separated.
Figure 14: Loop to loop coupling with 1 cm spacing.
The problem is that using a shielded loop can sometimes give a false sense of security that electric field effects are not important. Parasitic capacitance coupled to a shielded magnetic loop can affect its performance. In this case, a resonance was caused that significantly affected the signal induced into a second shielded magnetic loop.
CASE 1: Coupling to a PCB
A case is shown where using a shielded loop to inject signals into a path on a circuit board results in a significant resonance whereas using an unshielded wire loop results in a relatively flat frequency response of the injected signal.
Figure 15(a) shows a square unshielded wire loop held up to a path crossing a break in the ground plane of a test board. The injected signal was measured at the BNC connector on the board (left side) for the cases where the loop is positioned as shown and for a 180 degree rotation of the loop and similarly for a square shielded loop, embedded in plastic for strength, as shown in Figure 15(b). Figures 16(a) and 16(b) (page 84) show the measured signal at the BNC connector on the board for the unshielded wire loop in the normal position and for the 180 degree rotated position of the loop respectively. The data was taken using an Agilent N1996A spectrum analyzer as a two port insertion loss measurement. The square loop was connected to the tracking generator output and the BNC connector on the board was connected to the receiver input of the analyzer.
Figure 15: Coupling into a circuit with loop: Unshielded (left) and Shielded (right).
Capacitive coupling between the loop and the board will cause either a resonance effect (dip or peak in the response) or a directional effect when the loop is rotated 180 degrees because the phase of the inductive coupling changes by 180 degrees whereas the capacitive coupling remains the same.
As can be seen in Figures 16(a) and 16(b), there is no resonant effect, the frequency response is nearly flat. The capacitive coupling itself is very low compared to the inductive coupling because the difference is only a few dB and then only at the higher frequencies above 600 MHz.
Figure 16: Injected signal for unshielded loop normal orientation and reversed 180º
Contrast the responses for the unshielded loop to the responses in Figures 17(a) and 17(b) for the shielded loop. In both Figures 17(a) and 17(b), a resonant dip in the response is seen similar to that shown for coupling between shielded loops in part V. In this case, the resonance is due to the sum of the inductance of the shields of the loop and the inductance around the split in the ground plane interacting with the capacitance between the shields and the ground plane of the board. As one would expect for a shielded loop, the plots in Figures 17(a) and 17(b) are not very sensitive to the normal and rotated positions of the loop.
Figure 18: Measuring the coupled signal into a circuit in the time domain
One can conclude from the above plots that the unshielded loop works better for injecting signals into a path crossing a ground plane split than does the shielded loop. Surely this result holds in general for injecting signals into circuit boards with ground and power planes.
CASE 2: Measurements in the Time Domain
A case is shown where using both unshielded and shielded magnetic loops to inject signals into a path on a circuit board results in an injected signal that is about the same for both loops. Figure 18 shows a square unshielded loop held next to a path crossing a break in the ground plane of a test board.
The injected signal from a Fischer Custom Communications TG-EFT pulse generator connected to the loop was measured at the BNC connector on the board (left side) using an oscilloscope for cases where the loop is positioned as shown and for a 180 degree rotation of the loop. Bandwidth of the oscilloscope used was 500 MHz and the TG-EFT was set to generate open circuit pulses of 100 V with a rise time of about 2 ns and pulse duration of about 100 ns.
Figures 19(a) and 19(b) (page 86) show the results as displayed on the oscilloscope using the unshielded loop oriented in the both positions parallel to the path over the break in the ground plane, 180 degrees rotated from each other.
Figure 19: Injected Signal for normal and reversed unshielded loop.
Both plots have about the same pulse shape, amplitude, and width. Any change between the plots might be attributable to capacitive coupling, however, the only difference of any note is that the rise time in Figure 19(a) is a little faster than in Figure 19(b). The overall difference in the plots is not significant enough to make much difference when using pulse injection for troubleshooting designs.
The plots in Figures 20(a) and 20(b) for the shielded square loop are also very similar as well as having about the same rise time for both plots. The amplitude of the injected pulse is about 20% less because the distance between the center conductor of the semi-rigid coax forming the loop is further from the path on the circuit board due to the diameter of the coax and the thickness of the plastic housing. The slight improvement in matching of rise times is not significant enough to warrant the extra complication and cost of shielded loops. In addition, if the scope had greater bandwidth, the resonance at about 600 MHz between the shielded loop and the board would likely cause distortions in the pulses displayed in Figure 20.
Figure 20: Injected Signal for normal and reversed shielded loop.
Capacitive coupling from an unshielded loop is not always a problem that requires the use of shielded loops to solve. On the contrary, unshielded loops often work as well as shielded loops as was demonstrated by pulse injection in this example.
This article on square shielded loops has shown that unshielded loops are useful in many cases and for injecting signals into circuit boards specifically. Unshielded loops can even outperform shielded loops in some applications. Given the ease of constructing an unshielded loop and its low cost, this is an important result.
- Smith, Douglas C. 1992. High Frequency Measurements and Noise In Electronic Circuits. New York: Van Nostrand Reinhold. ISBN #0-442-00636-5.
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- EMCO. 1999. User’s Manual Near Field Probe Set Model 7405. REV E-PN399107.
- Smith, Douglas C. 1993. High Frequency Measurements and Noise in Electronic Circuits. New York: Van Nostrand Reinhold. ISBN 0-442-00636-5.
- Smith, Douglas C. 1997.“A method for troubleshooting noise internal to an IC.” IEEE 1997 International Symposiumon Electromagnetic Compatibility: 223-5.
- Smith, Douglas C. 1999. “Signal and noise measurement techniques using magnetic field probes.”IEEE 1999 International Symposium on Electromagnetic Compatibility: 559-63.
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|Douglas C. Smith
Mr. Smith held an FCC First Class Radiotelephone license by age 16 and a General Class amateur radio license at age 12. He received a B.E.E.E. degree from Vanderbilt University in 1969 and an M.S.E.E. degree from the California Institute of Technology in 1970. In 1970, he joined AT&T Bell Laboratories as a Member of Technical Staff. He retired in 1996 as a Distinguished Member of Technical Staff. From February 1996 to April 2000 he was Manager of EMC Development and Test at Auspex Systems in Santa Clara, CA. Mr. Smith currently is an independent consultant specializing in high frequency measurements, circuit/system design and verification, switching power supply noise and specifications, EMC, and immunity to transient noise. He is a Senior Member of the IEEE and a former member of the IEEE EMC Society Board of Directors. His technical interests include high frequency effects in electronic circuits, including topics such as Electromagnetic Compatibility (EMC), Electrostatic Discharge (ESD), Electrical Fast Transients (EFT), and other forms of pulsed electromagnetic interference. He also has been involved with FCC Part 68 testing and design, telephone system analog and digital design, IC design, and computer simulation of circuits. He has been granted over 15 patents, several on measurement apparatus.Mr. Smith has lectured at Oxford University, The University of California Santa Barbara, The University of California Berkeley, Vanderbilt University, AT&T Bell Labs, and internationally at many public and private seminars on high frequency measurements, circuit design, ESD, and EMC.He is author of the book High Frequency Measurements and Noise in Electronic Circuits. His very popular website, http://emcesd.com (www.dsmith.org <http://www.dsmith.org> ), draws many thousands of visitors each month to see over 150 technical articles as well as other features.He also provides consulting services in general design, EMC, and transient immunity (such as ESD and EFT), and switching power supply noise. His specialty is solving difficult problems quickly, usually within a couple of days. His work has included digital and analog circuits in everything from large diesel powered machinery to IC chip level circuits. His large client base includes many well known large electronic and industrial companies as well as medium sized companies and start-up companies.
Arturo Mediano received both his M.Sc. (90) and Ph. D. (97) in Electrical Engineering from the University of Zaragoza, Spain where he has held a teaching professorship in EMI/EMC/RF since 1992. He is member of the Group of Power Electronics and Microelectronics (GEPM) of the Aragon Institute for Engineering Research (I3A).Since 1991 he is working in EMI, EMC and RF (HF/VHF/UHF) fields for communications, industry and medical applications with substantial experience in collaboration with industries, focusing on training, consulting, design and troubleshooting. He is Instructor of Besser Associates (CA, USA), offering periodically public and on-site courses in EMI/EMC, Signal Integrity (SI) and RF subjects through the USA, specially in Silicon Valley/San Francisco Bay Area and he has taught tens of RF/EMI/EMC/SI courses through Europe. He was Invited Lecturer for the École Polytechnique Fédérale de Lausanne (EPFL) in Lausanne (Switzerland) and for the Institut National des Télécommunications (INT) in Evry (France).He is author/co-author for many publications and patents and a frequent speaker in the most important symposiums and conferences related to RF/EMC. Arturo is Senior Member of the IEEE, member of the EMC Society (ESAC Committee), and member (Chair since 2013) of the MTT-17 (HF/VHF/UHF technology) Technical Committee of the Microwave Theory and Techniques Society. Arturo shares free time between his family, fly fishing, and drawing cartoons.