Last revision 1 June 2010
Wideband Active Small Magnetic
This paper is an addendum to previous article http://www.lz1aq.signacor.com/docs/wsml/wideband-active-sm-loop-antenna.htm 
1. Practical circuit
The schematics of the antenna amplifier  is not changed only a protection is added. The practical protection circuit is shown on Fig.1. It consists of diode limiter (D1 to D8) which limits the differential input voltage and common mode limiter (D9 D12) which limits the common mode voltage to safe values. Parallel diodes connection is used to increase the safe limits. This active loop will not be damaged if the distance to the transmitting antenna is more that 10-15 m for legal limit transmitting power (1- 2 KW). In the cases where the loop is placed very closely to the transmitting antenna an experiment should be drawn to obtain the actual values of induced currents (see Calculations part).
Theoretically this circuit probably will withstand nearby lightning strike (distance 100m and more). The induced voltages up to 200 V from the magnetic pulses and electric field pulses up to 50kV/m can be assumed as an upper limit. For continuous fields (as from nearby transmitter) field intensities up to 500 V/m might be assumed as safe.
Fig.1 Practical protection circuit for active wideband small magnetic loop.
There is a protective ground connection for the protection of high common mode electric fields. This connection can be a small rod inserted into the soil. If it is not possible to have a nearby ground the protective point can be connected to the shield of the FTP cable thus eliminating the possibility for high voltage differences between antennas and receiving equipment.
I will take a real example to compute the input currents and voltages in a wideband active magnetic loop when it is exposed to high intensity electromagnetic field. The only protection is a diode limiter which is placed parallel to the terminals of the loop. I have used LT spice for modeling but in the simplest cases the calculations are quite simple.
2.1. Strong field from nearby transmitter
Far field zone
The example loop has 1 m diameter with single turn made from 3.5 mm diam. aluminum wire. Its inductance is 3.6 uH. The Norton equivalent circuit of the loop is used (Fig.2) since it is frequency independent. The wideband amplifier saturates at very low (50mV) input voltage, so there is no need to use more diodes or any negative bias voltage. For simplicity the amplifier input transistors are not included in the model - if the limiter currents are not exceeding some limits we are sure that there will be no harmful voltage the rest of the circuit. Let us assume that the antenna is in the far field zone and the field intensity is 100 V/m. This is very high field strength we should be aware that the safe limits for human exposure to electromagnetic field by most of the standards are between 3 to 10 V/m. Using the Excel spreadsheet given in the article http://www.lz1aq.signacor.com/docs/wsml/RX_Mag_Loop.xls we will obtain that the short circuit loop current is I = 70 mA. This current does not depend from the frequency. The spice model shows that the peak current flowing through the diodes will be less or equal to 70 mA. If the diodes are omitted the voltage across the loop terminals will be 7 V.
What all these calculations mean? I calculated that 100 V/m is the field intensity at 40 m distance from 500 KW transmitter with an isotropic antenna in free space. That is equal to 5 KW transmitter with beam antenna with 20 dBi gain! 1N4148 can withstand easily 70 mA current. According to 1N4148 data sheet it can withstand 200mA continuous current and 1 A current for 1 second and 4 A for 1 uS. Even if there are no limiting diodes the amplifier will probably not be damaged.
Near field zone
The previous example shows that harmful voltages can occur only in the near field zone of the transmitting antenna. It is difficult to estimate roughly the induced currents in the loop when the loop is very close to the transmitting antenna in so called near field zone since the calculations are not simple and depend very much from the particular geometry of the setup.
I will suggest a simple test remove the amplifier and put 100 ohms resistor as a loop load. Connect there simple RF peak voltage detector and measure the induced voltage (Fig.3). Turn the loop to position of maximal voltage. For voltage indicator use analogue meters with very short leads. Standard DVM might not work since the RF field might influence their readings.
Another way is to put a super-bright red LED to the 100 ohms trimmer resistor. As shown on Fig.4. The red LED opens at 1.8 volts and began to be visible when the current is 100-200 uA (for super bright LEDs). Adjusting the LED to shine weakly and measuring the values of the resistive divider the actual current from the loop can be calculated. The LED indicator is very convenient since it can be watched remotely in the night time so the man is not exposed to high field intensity.
I have made an experiment with 100w transmitter and dipole antenna on 3.5MHz. The loop was at 5 m from the far end of the dipole and the LED does not blink in any position of the trimmer.
We should be aware that the intensities in the near filed zone depend from the distance d with law 1/d2 or even 1/d3 so every meter distance is important.
Precaution: Use minimal transmitting power to obtain experimental results since the safe human limits might be surpassed! Then extrapolate the results for the full power case bearing in mind that increasing the power 2 times increases the currents or voltages 1.41 times ( by square root law).
2.2 LIGHTNING Strike
The field intensity of nearby lightning strike is much higher. The maximal field intensities are associated with so called return stroke in ground to cloud discharge. Cloud to cloud discharges have smaller intensities. There are very interesting published data for the field intensity at close distance to the lightning discharge [1, 2, and 3]. The field intensity is measured accurately for the natural lightning strikes. The return stroke electric field pulse shape is given on Fig.5a and the magnetic filed pulse is given on Fig.5b. . The magnetic field pulse follows the discharge current and is very sharp. The electric field has much different behavior (Fig.6) it rises slowly (several milliseconds) and at the time of discharge there is a fast slope.
Fig.5 Typical patterns of the field pulse during the lightning discharge (microsecond scale).
Time 0 is the discharge occurrence. From  J. Jerauld et al.
Fig.6 Electric field changes at different distances from the natural lightning discharge (ms scale).
Time 0 is the discharge occurrence. From  J. Jerauld et al.
The loop antenna is a magnetic transducer which is sensitive to changes in the magnetic field. The antenna is in the near field zone of the strike and data for magnetic field intensity should be used. The induced voltage can be calculated by the Faradays law - E = - dÔ/dt . The equivalent circuit is shown on Fig.7 .
Fig.7 Spice model of the protection circuit for magnetic pulse stroke.
The correct physical model is a circuit with serial voltage source. Again the loop is 1 turn with 1 m2 area and we can use directly magnetic induction B instead of magnetic flux Ô. The loss resistance of the loop is chosen to be 1 ohm somewhat arbitrary. The induced voltage is a derivative of the magnetic induction B (Fig5b) and the peak amplitude is in the rising edge. The voltage V [in volts] is equal to dB/dt in T/s - [ tesla per second].
Fig.8 dB/dt pulse, measured at a distance of about 72 m from the flash. From  J. Jerauld et al.
There is some uncertainty especially for the rate of change of the magnetic field when using the published data in graphical form. In the same paper  there are statistical data (Table12 in ) from where some approximate calculations can be performed to estimate the magnitude of dB/dt.
Distance to lightning: 100-200m 200-400m 400-800m 800-1000m
Peak dB/dt [T/s] 45 12 10 8
Front duration of B [uS] 0.5 1.6 1.6 1.6
For very near zone the dB/dt peak value can reach very high magnitudes (Fig.8). In  at 15 m distance values from 400 up to 2000 T/s and rise times between 20 to 100 ns are given.
For the spice model we will assume that the shape of dB/dt pulse has a triangle form (Fig.8 is dB/dt waveform of a natural strike) with rising and falling edge ½ from the front duration of B pulse. A triangle pulse with 0.25 us fronts and 100 V peak value is used for the calculations. These values are 2 times stronger than the values given in Table 1 (first column). The calculated peak current through diodes in this case is 6.2 A. The shape of the current pulse is shown on Fig.9. The peak pulse current is limited by the inductance of the loop L (3.5uH) and the loop loss resistance R4.
Fig.9 Results from LT Spice model. Input is a 100 V pv dB/dt triangle magnetic pulse (red).
Peak diode current is 6.2A (green). Blue is the output voltage across R5.
Common mode voltage
The antenna amplifier is also exposed to common mode voltage due to the electric field component during lightning strike. The amplifier is a balanced circuit and it is no good idea to connect the amplifier common point to ground since the common mode current might be increased substantially thus reducing the immunity to the local noise. In normal conditions the amplifier should not have undefined ground loop paths. Fig.10 presents the common mode equivalent circuit along with suggested protection.
Fig.10 Spice model of the protection circuit for electric pulse stroke.
The loop antenna is now equipotential point A for electric filed and it can be modeled like a short whip. The equivalent circuit is a voltage source and 20 pF capacitance. The protection consists of two zener diodes which are used to clamp the high voltage to ground. The leakage resistor is used for continuous leakage of the antenna electrostatic potential due to atmospheric phenomena (rain, snow etc.). In normal conditions the diodes are closed and the common point of the amplifier is connected to ground only through the leakage resistor and the diode capacitance which is on order of 1-2 pF. The model of E field again is a triangle pulse with slow rising edge of 5ms , followed by fast edge with 0.5 us duration (see Fig.6). The peak value of E is assumed to be 50 KV/m which will give the equivalent voltage V1 of 50KV if the antenna has 1m effective height.
The spice modeling shows that the peak current though zener diodes will be 2A for 0.5 us duration at the discharge edge. Here the stress to the diodes is much smaller and ordinary 0.5W zeners can do the job.
For legal limit transmitting power (1- 2 KW) and standard antennas the active wideband loop using the proposed protection circuit will not be damaged if the distance is more that 10-15 m. In the cases where the loop is placed very closely to the transmitting antenna an experiment should be drawn to obtain the actual values of induced currents.
The protection from possible nearby cloud-earth lightning strike less than 100m from the discharge zone is questionable. The good think is that such a near strike is a rare phenomena most of the people will never have such an accident. There is some uncertainty in my analysis since it use some extrapolated data for the rate of magnetic field change which is the main parameter to calculate the induced voltage. There is a tendency that the closer is the strike the steeper is the B front. The induced voltage from wideband small magnetic loop in high magnetic field intensities is relatively low but the problem is that the equivalent source is with very low internal resistance and substantial currents can arise. From the other hand the inductance of the loop itself began to limit this current in the case of very steep pulses. In order to improve the protection for very near strikes a better limiter is needed. What is needed is a fast ( at least 20 ns) low capacitance ( <20pf), high pulse current (>20 A for 1 us) low voltage limiter. The gas discharge tubes are not very suitable in this case. Their switching time is between 2 to 20 us. Paralleling fast switching diodes such as 1N4148 is a reasonable way to increase the maximal allowable current. On the market now there are numerous fast and powerful switching diodes and TVS which might be used for the limiter but for the moment I have not find any suitable device.
The lightning protection part must be assumed as a suggestion which is not proved experimentally since I do not have an access to suitable lightning equipment : ) . As a final comment we must be aware that in the case of very near strikes secondary effects can arise (e.g. induction in connecting cables, unexpected current paths etc.) and this might destroy any protection circuit.
- This analysis does not refer to the case of tuned loops.
- This amplifier saturates in the case of strong fields and its clipping output level is approximately 6 V pp at the 50 ohms load. Most of the analog RX will withstand this voltage without problems. Look carefully at the specifications of the direct sampling SD Radios for maximum allowable input voltage.
- Be aware that Mother Nature can always surprise us.
Chavdar Levkov, LZ1AQ
 J. Jerauld, M. A. Uman, V. A. Rakov, K. J. Rambo, D. M. Jordan,and G. H. Schnetzer. Electric and magnetic fields and field derivatives from lightning stepped leaders and first return strokes measured at distances from 100 to 1000 m. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D17111 , 2008, http://www.lightning.ece.ufl.edu/PDF/Jerauld_et_al_2008a.pdf
 , V.A. Rakov, CHARACTERIZATION OF LIGHTNING ELECTROMAGNETIC FIELDS AND THEIR MODELING. University of Florida, Gainesville,USA, http://www.lightning.ece.ufl.edu/PDF/Zurich/1T01.pdf
 J. Schoene, M. A. Uman, V. A. Rakov, V. Kodali, K. J. Rambo, and G. H. Schnetzer. Statistical characteristics of the electric and magnetic fields
and their time derivatives 15 m and 30 m from triggered lightning. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D6, 4192, 2003, http://www.lightning.ece.ufl.edu/PDF/Schoene_et_al_2003a.pdf
 Chavdar Levkov, LZ1AQ, Wideband Active Small Magnetic Loop Antenna, 2010, www.lz1aq.signacor.com