pifa efficiency

I want to design one PIFA and first of all I need to decide my substrate material. Therefore, I simulate one PIFA with three different substrate permittivities: 1.0, 2.2 and 3.48. Meantime, the loss tangent of substrate is assumed to be zero. The simulation results of the radiation efficiency are as follows:
er=1.0: 85%
er=2.2: 45%
er=3.48: 20%

The simulation setup and structure under simulation are all the same except er. The decreasing trend of rad effi is reasonable. I just wonder why there is such a large drop. According to a rough analysis, it's not difficult to find that any possible loss should be low (due to metal conductivity and surface wave, no dielectric loss). So the dramatic change at rad effi with er is because of the change of the radiation resistor. And according to the the radiation conductance formula based on the transmission line model of microstrip antenna, I think the rad resistor alone can not make such a big difference.

Any comment? Is the low rad effi like 20% common among PIFA designs with medium substrate permittivity?

It shouldn't be that low. I had designed an antenna on a Er = 3.6 substrate and the radiation eff was about 60%.

You should consider the following points:

1. Do you observe the eff. at the same frequency for all 3 substrates? Since you change your substrate but not your structure, your resonance frequency is changed. You should look at the new resonant frequency to compare those.

2. Do you observe radiation eff. or total eff.? total eff. includes the mismatch loss the the input port. I don't think you measured total eff. however, just to make sure :D

Hi, streamlet:

If your substrate is large in the xy direction, the loss might be due to the surface wave. Surface wave can be quite big when the substrate thickness is too big.

I also noticed that PIFA can be very low efficiency when the size of the structure is electrical too small. In fact, I noticed that some designer is able to optimize a PIFA-like antenna with very close shorting pin and feedining probe and the antenna size is much smaller than quarter wavelength with good resoannce. However, the resonance is mainly due to the metallic loss instead of radiation. It is still not a good antenna because the radiation is very low even the size is very small and the resonance create very low return loss. Regards.

to shameemkabir:
1, I have noticed this, so in fact i got their radiation efficiency both at resonance and at the frequency (0.9GHz) intended to be working at. They appear the same trend. Details are as follows:
er=1: 95% at f_resonance=1.5GHz
85% at f_intended=0.9GHz
er=2.2: 40% at f_res=1.1GHz
45% at f_int=0.9GHz
er=3.48: 20% at f_res=f_int=0.9GHz
20% at f_res=f_int=0.9GHz

2, As you have already seen, i observed the rad effi instead of total effi.

Added after 13 minutes:

to jian:
I am using IE3D to simulate my PIFA
The cut off frequency of the TE1 mode surface wave
is calculated to be 12.5GHz for er=3.48 and substrate height=3.81mm, which is far larger than my intended frequency 0.9GHz.

Besides, I use the formual presented in D.M.Pozar's "Rigorous closed-form expressions for the surface wave loss of printed antennas" to have an estimation rad effi about 92% including only surface wave loss. According to the above two facts, I think the surface wave is not a major loss source.

As for the antenna size, I confirm that my PIFA complies with the quarter wave rule, in other words, it is not electrically small when er=3.48.

Hi, streamlet:

I am not sure about your statement "the cut-off frequency of the TE1 surface wave mode...". Frpm my understanding, surface wave does not have any cut off frequency. It will be there no matter how thin the substate is. The question is how large it is. I don't think there is any good analytical formula to estimate it. In fact, the surface wave loss is not only related to the substrate thickness, it is also related to the shape of your structure. A PIFA may have a relatively thick substrate. Also, the shorting pin and other vertical structures may create much surface wave. Regards.

hi, jian
Yes, there is always surface wave existed no matter how thin the substrate is as long as the sub permittivity is larger than 1. That kind of "ever-lasting" surface wave is designated as TM0 mode. Other higher mode surface wave will be excited above their cut off freqeuncies. The TE1 mode surface wave is the second most possible type of surface wave.

My PIFA's thickness is 3.81mm with er=3.48. And its structure is quite simple, no any complicated tuning mechanism has been used yet, since it's just at a pre-study stage.