Miniaturizatied Antenna

Does miniaturization means shifting of resonance frequency towards low-side? or reduction of the antenna size?.....How to calculate miniaturization factor for an antenna?...If it is related to antenna size how to determine its miniaturized length?....Is it a parametric procedure?? Kindly help me friend!

A Miniaturizatied Antenna is just one that is smaller then you would expect for its performance. It is the holy grail of aerial design, being able to make a smaller (and hence cheaper and more convenient). But is essence you just trade one parameter for another.
If you were aware of the TV aerial on top of the World Trade Centre that collapsed, that was a miniature aerial. This was because of the limitations of the WTC structure a full sized UHF TV transmission aerial was not possible, so the aerial was smaller BUT they needed ten times the number of transmitters to get the same range as a conventional array.
Frank

I use them all the time. BUT it is a love/hate relationship.

In general, you take an antenna shape that is MUCH shorter than the length needed to get it to resonate at. Then you add some reactive element to make it resonate ON-FREQUENCY that is the center of your passband. So for a quarter-wave whip antenna, you make the whip maybe one-third of a quarter wave long physically, but put a large inductance value between the ground plane and the base of the whip. Electrically....the combination of the inductor and 1/12th wavelength long whip wire equals 90 degrees, and it resonates. You simply capacitively couple to the whip somewhere above the inductor to get the best 50 ohm match.

But to work like this, there are going to be big resonating currents flowing on that inductor and whip. So first the inductor has to be able to handle those currents. 2nd it needs to be a high Q inductor to minimize the losses. and finally, even with a high Q inductor, you will find that its radiation efficiency is severely compromised. i.e. even though the VSWR is low...it does not have the gain you were hoping for. For my example of a 1/12th wave base loaded whip, I would not be surprised if I measured an effective gain of perhaps -9 dBi.

maybe a real antenna guy could comment on why these electrically short antennas do not couple to the air very efficiently from a theoretical sense?

Reducing antenna length with half, doubles its resonance frequency.
A shortened antenna can be retuned to original frequency with aid of reactive components, but it comes at a cost.

For a rough estimation, assume:
Natural resonant dipole length (0.5 lambda) = 1
Radiation efficiency for 0.5 lambda dipole = 100%
Short dipole length ratio, L < 1 relative full dipole length.

Radiation efficiency for short dipole [%] = L² * 100

Radiation resistance follows same ratio.
It assumes ideal impedance matching. Due to ideal matching is bandwidth reduced.
Matching with lossy real components for low losses in matching network is complicated when radiation resistance is a fraction of 1 Ohm.

Assume a short dipole, 0.05 lambda, or 0.1 of a full dipole length:
Radiation efficiency is 0.1*0.1 *100 = 1% (-20dB), relative a 0.5 lambda dipole, and lossless impedance matching is assumed.
Radiation resistance is 73 *0.01 = 0.73 Ohm

For a bit more correct formulas, search for Hertzian dipole.

Antenna space in a smartphone, is a fraction of actual wavelength and often poor located due to display size, battery size and height above PCB ground is low.
Antenna space can be even smaller then calculated above, indicating less then 1% efficiency, but measured efficiency can be as high as 70% at 900 MHz in phones with the good performing antennas.
Reason is that antenna is a monopole and PCB ground is used as the other part required to form a dipole antenna so actual antenna size is almost whole phone length.
It is still complicated to design a good antenna structure and a fitting low loss tuning network. Their impedance curves must complement each other over a wide wideband and multiband. Some phone designs fails big. Have measured phones with antenna efficiency less then 20%, or 10 dB below the best phones.
If base-station coverage is good is that seldom a big problem but if living a bit rural can it be of a notable difference in coverage or dropped calls.

Patch resonators use higher dielectric constant substrates than free air, so λ is shorter.

Yes higher dielectric material, e>1, which is everything except air, shortens lambda length. Effect of this can be seen in a cellphone. Bigger structures such as PCB, display and battery all effect total antenna impedance due to its dielectric constant, when these parts are a part of antenna structure.
Ceramic antenna structures with e above 30-40 can radically reduce antenna PCB footprint at cost of bandwidth. There are also some other antenna structures that can be made resonant at sizes much less then 0.5 lambda, such as small loop antennas and antennas with a ferrite core.
In general, reducing antenna size with or without high dielectric material is at cost of bandwidth and/or efficiency. Narrow bandwidth is sometimes not a problem, such as for GPS and even BT and if wider bandwidth is needed can active tuning be used.
Smallest possible embedded antenna for a certain performance is often a question about a total design concept. Is PCB groundplane stable and big enough to be used as part of the antenna, can resulting RF ground-current cause interference with low frequency signals, available amount of antenna volume, what shape do it have, what material will enclosure have, handheld, directivity..

TS asked how to calculate miniaturization factor for an antenna. Length is a obvious factor which have been given examples for a short dipole but antenna miniaturization factor is not only in terms of length. Needed volume for antenna structure and needed volume around antenna that must be free for a certain performance is in a real design that should be compact is just as important but parameters and needed calculations are way to complex to describe in few simple lines. Can recommend a lot of heavy books if TS really want to learn about such parameters.

If designing commercial embedded antennas is cost a main miniaturization factor for how small antenna to design. Cost comes in a lot of shapes.
Main cost is antenna volume, I do not understand why but design department says that when all other electronic components becomes more compact with better performance for each year, must that include antenna.
Active tuning cost increased complexity and cost for added components. Using high dielectric ceramic material adds cost of weight and money. Flexfilm antennas adds cost for carriers and connectors. Often is it a bit opposite, small sized material cost more money then big structures.

Another miniaturization factor is total size, not of antenna, but of final product. An antenna is seldom a stand alone product.
A common design mistake is to not leave enough space for antenna in a small TX something and maybe due to too small space get a resulting antenna efficiency below 10%. For a expected coverage must then TX power be increased and for not loosing battery lifetime due to increased TX power, must battery size be bigger and heavier. This poor performing antennaa will cost more development time as every tenth of a dB must be found to make product as acceptable as possible.
Leaving bigger space for antenna can result in a total smaller, less heavy and less power hungry product.
However almost always is antenna something included late in design phase, "Oh yes, we have forgot an antenna, but there is a small space where nothing else fit. Tell antenna-guy to design a top performing antenna in that shape".
So it is design department that invent small antennas. As antenna-guy you only have to fill that space with something.

"Short" aerials always look capacitive, so a series inductor is required to get them to resonate to the required frequency, this raises the Q and so reduces the bandwidth. Conversely the raising of the Q increases the circulating current in the circuit and the losses of the inductor.
I once worked on a airport landing beacon, these operated on 210-400 KHZ but because of the airplanes, could not use a full quarter wavelength aerial (375 - 700 m !!). The aerials were 5m whips. The transmitters could put 80W into a 50 ohm load, but only 10 W into the 10 ohm+ 100 PF load. The balance of the power being dissipated in the series inductor despite it being VERY special with a Q ~500. So this is another problem with "miniature" aerials.
Frank