# Is the Friis Formula outdated?

It looks to me like the Friis formula is outdated. We can replace it with the E and H near field formulas, that converge into the same value in the far field.

I found it hard to use the Friis formula, whenever I switch from nearfield into farfield move, there is a sudden 20-30 dB error lag between the nearfield value and the farfield value. I don't think there is any kind of boundary that just does that, I think the values smoothen out and slowly converge.

So basically the Fraunhofer Boundary λ / (2 * π ), is a very stiff method to figure out the edge of the farfield, and it's prone to a lot of error. I think it's outdated.

Instead using the nearfield formulas introduced by Dr. Hans Gregory Schantz, seems like a more smooth way of looking at things: It certainly works in the nearfield, it was verified by experiments. And there is no reason why it would not stretch into the far field. And basically the far field instead of becoming a stiff boundary like the Fraunhofer Boundary, it becomes like a smooth convergence point: In this test I simulated a 2x 1 m long antennas 50 m distance from eachother, but it's like this for any other parameter.

As you can see if we go with the Fraunhofer Boundary using the Friis formula, the Farfield starts at 1.2 Mhz, however the nearfield formulas didn't converged yet, nor there is a concrete point of convergence. It looks like the Farfield Boundary at this case starts more like at 104.6 Mhz.

So it looks like the Fraunhofer Boundary is an obsolete concept, I think it's more dynamic than that, and there is no boundary, I think the impedance differences just smoothen out as frequency increases until it slowly reaches the free space impedance.

Edit 1: Sorry actually, the "d" in the formulas represents the distance between the transmitter and receiver, not the boundary sphere.

Edit 2: And the Fraunhofer Boundary doesn't start exactly at 1.2 Mhz, but somewhere between 806 Khz and 1.2 Mhz, I didn't calculated the exact frequency. However it doesn't matter, either way, there is still a high difference between the 2 fields's path loss. So I guess the far field starts when the impedance reaches that of the free space, which is more like at around 104.6 Mhz.

• Maxwell worked out the field patterns in his original Thesis on Electricity and Magnetism and plotted them with spherical 2nd, 3rd and 4th order effects for near field emitters based on static charge which can be used for alternating charges.. So the assumption Friis formula which works only for far field assumes an 2nd order effect only as elliptical radiator with gain or a spherical isotropic radiator, rather than 1st order plane wave or 3rd, 4th order torroidal near field effects. they are hand drawn with great resolution in the appendix and book can be found on archive site – Tony Stewart EE75 Jul 16 '17 at 16:18
• you must avoid Avoid Ricean Fading errors in open field or between rooftops to avoid near field errors. I did this on my 1st rocket antenna design test in '77. Magnetic field measurements are complex in near field , so be aware of reflections. – Tony Stewart EE75 Jul 16 '17 at 16:22
• @TonyStewart.EEsince'75 I don't think this formula is like engineering grade precision, it obviously doesn't count in the reflections or the angle of incidence, polarization, nor the fact that in the near field the standing wave can bond to other metalic objects. I think that would require a lot of complex calculations. This is just a general formula for day to day use. – David K. Jul 16 '17 at 16:39
• I wonder what formulae they use for WPT charging of E-vehicles with 11kW 200kHz at 22cm gap with up to 80cm diam. loop I Wonder what the coupling impedance is perhaps lower than 377 Ohms but much higher than ESR of battery charger loads. so impedance matching is the key to antenna coupling by resonance I expect and/or turns ratio step down voltage with RX autotransformer to step down or dependent on choice of antenna impedances Series or Parallel. – Tony Stewart EE75 Jul 16 '17 at 17:04
• The table of attenuation implies that E/H=1 drops rapidly meaning the coupling impedance Z(f) rises sharply as f reduces at fixed distance d or reduced d at fixed f, meaning near-field. This is significant. perhaps related to ωL/R ratio or high order (4th,6th) effects of gap on E field. – Tony Stewart EE75 Jul 16 '17 at 17:53

## 3 Answers

Is the Friis Formula outdated?

Well, you probably can say the Friis formula doesn't work so well when the EM wave hasn't fully formed and the impedance (as E/H) isn't 377 ohms but, it's not expected to work that well in the near field or on the borderline.

So, is the Friis formula outdated? No, because in the far field it works as expected and will be continued to be used.

Have you shown that another formula is simpler in the far field? I can't see that you have. Have you shown that another formula is more accurate in the far field? No I can't say that what you have said is convincing.

I would be very interested to see how the two formula outcomes converge mathematically (or numerically) but I'm unsure that your table is demonstrating that. Maybe it isn't meant to demonstrate that?

Another thing that puzzles me about the table of numbers is that you haven't demonstrated that you have factored-in the fixed antenna length of 1 metre. Clearly, at about 75 MHz a quarter wave monopole is tuned at 1 metre length but, like I said, your table doesn't show how you have factored this in at lower frequencies where it's impedance becomes very capacitive.

Don't get me wrong on this, I'm not trying to be picky; I'm just trying to understand what your table fully reflects in the real world (not that the friis equation is all-together real-worldly).

• Well it might not be simpler, but it definitely is more accurate. The Friis formula depends entirely on the detection of the Fraunhofer boundary which is a very stiff way of looking at it, the λ / (2 * π ) definition is the rule of thumb, but it still could be wrong. Thomas Kaiser says that the impedance becomes 377 at 5λ / (2 * π ), but who knows maybe this isn't that correct either. I think a more flexible smooth approach is needed. So I think these formulas are good for that. It should be more analyzed, but so far I haven't seen any other papers on it, from perople other than Schantz. – David K. Jul 16 '17 at 16:18
• "Another thing that puzzles me ... " , well I have used the "Boundary Sphere" concept introduced by Wheeler and Chu. It's basically the smallest diameter sphere that completely surrounds an antenna. So we have 2 boundary spheres with 1 meter diameter, 50 meter away from eachother. Of course this is a rough model, but it kind of works. – David K. Jul 16 '17 at 16:24
• I'm not disagreeing - I'm just saying that you haven't convinced me. For instance, beyond 100 MHz it seems that your final column (which I think is the friis calc) is pretty much the same as what Schantz's formula says. Also, higher gain antennas have a much extended near-field so a one-size fits all for the boundary isn't that useful. – Andy aka Jul 16 '17 at 16:24
• "For instance, beyond 100 MHz it seems that your final column (which I think is the friis calc) is pretty much the same as what Schantz's formula says" Well yes the distance is fixed, only the frequency changes in this simulation. This is just to show how the 2 pathlosses converge. – David K. Jul 16 '17 at 16:27
• "Also, higher gain antennas have a much extended near-field so a one-size fits all for the boundary isn't that useful." I have used the fundamental max gain limit , on both the TX and RX antennas. You can't have a gain higher than what is inserted in this simulation of mine unless the law of energy conservation is broken. I think you misunderstood what the "Boundary Sphere" means, it's not the nearfield boundary, it's the physical boundary of the antenna. – David K. Jul 16 '17 at 16:30

From what I recall from Corsine and Lorraine (my copy is lent out), the coefficients atop (kd)^2, (kd)^4 and (kd)^6 are NOT ONE.

• it appears to be 1 in his publication goo.gl/2z9rD6 – Tony Stewart EE75 Jul 16 '17 at 23:49
• @analogsystemsrf, I have the book, that book offers a more complex equation with more parameters like the incidence angle, in case of a magnetic antenna, the number of loops, time-averaged Poynting vector, and such. I think this is a more simple approach for general use. – David K. Jul 19 '17 at 13:28

The notion of applying fixed boundary sphere gains to the Friis equation will not work without other significant adjustments to the Friis formula. By fixing the length of the antennas, the directivity and efficiency of both antennas will vary with frequency and this effect is not shown in your rightmost column.

It would seem that if you are trying to demonstrate a single formula model that smoothly transitions from a near to far field application, then the independent variable for the left hand column should be distance and not frequency. This then also allows you to fix antenna gains without disrupting the Friis formula.