Noise figure versus input referred noise

If we use the specification for a low noise amplifier, invariably the noise performance is a Noise Figure. However, in a particular system design we calculated the input referred voltage that could be a limiting factor for the very first stage LNA. The issue was how to convert from the noise figure of a selected LNA ( from Analog Devices no less) to the input referred noise voltage to make sure the amplifier was being chosen correctly. Well here is the conversion at least in one form.

Note: The noise factor is simply 1 + NA/Ni. Ni is the noise power coming in from a 50 Ohm matched source and is equal to -174 dBm/Hz. ( Pretty standard usage).

The noise voltage being generated by the 50 Ohm source is vni=4.46E-8 Vrms/Hz. This can then be used to compare whether the amplifer will work with a particular noise figure ( from the expression 1 + NA/Ni).

Check and see if the number NA, the noise input referred power generated by the amplifier itself, converted from a voltage to power is acceptable or not. Must remember to use the impedance level of 50 Ohm. Simple?


Example: If the NF is = 0.8, then 1+ NA/Ni = 10**0.08 = 1.2 ( approx). We can calculate vna as above for vni.

Here is a note on input noise. It has been found that the -174 dBm/Hz should be modified to -162 dBm/Hz for the rural environment in the US and to -98 dBm/Hz for the urban environment. The -174 dBm/Hz is therefore a theoretical figure used to specify and calculate noise figures and noise factors!

Yes, another thought; we need to make sure that the derivation for the noise factor is elaborated: Here it is:

Noise factor F = SNRi/SNRo where i stands for input and o stands for output.

So = Si X G ( G = Gain)
No = [Ni noise power from the 50 Ohm source + NA, noise power generated by the amp].

F = [Si/Ni] / [GSi/G(Ni+NA)] = 1 + NA/Ni.

Also for other items of engineering interest go to our website at www.signalpro.biz.

Thermal modeling and analysis of devices and MCMs

Thermal modeling and analysis of devices and MCMs ( modules) is becoming very important in recent times. In years past, most of the thermal effort was based on the design of devices, and thermal analysis was built into the circuit simulators such as SPICE. The rest of the modeling based on the electrical analogs of heat transfer was well understood, and could be done in a fairly simple way. Today the situation is quite complex. As more and more performance is demanded from semiconductors ( individually ) and from MCMs ( multi-chip modules ), and indeed entire products, such as cell phones, the heat per area is rising towards the 500 W/cm squared limit. This is a lot of heat, and it is very difficult to use the old methods to model and understand these problems. Therefore thermal modeling is attacking these issues in electrothermal dynamics by using newer CAD tools based on FEM ( Finite element methods ) and CFD ( Computational Fluid Dynamics). A number of new thermal modeling tools have appeared on the market. Some are reasonably priced and others are not. Again you get what you pay for! Heat flow is based on the conduction, convection and radiation of heat ultimately. Thermal CAD tools model these processes in their own proprietary way. We have used a couple of these tools and find them fairly, ( and I mean fairly ) complex. So practice is neccessary. However, the results obtained are within the 20% error band. The accuracy of results also depend on the skill of the user! More on this topic as time goes on. It is a fascinating subject.

RF/MW ESD and complex matching using resonance

An interesting technique that finds extensive use in RF/MW ESD circuits and complex matching circuits is the concept of resonating out reactances. Taking the case of the ESD circuit we find that in the most usual case RF/MW ESD circuits ( as other ESD circuits do) use some form of diodes to protect sensitive inputs on an IC. This of course leads to a parasitic capacitance which causes loading and mismatches. In order to eliminate the effect of this capacitance, at a single frequency an inductor can be used in parallel with the parasitic capacitance. The value of the inductor is chosen to resonate with the parasitic capacitor and therefore at the resonant frequency the pair becomes invisible leaving only the resistive part to be matched or considered. This is a simple technique which finds wide application in a number of critical circuits. Obviously the limitation is the single frequency characteristic. However, with some subtle manipulations it can also be used in wider bandwidth applications.

Receiver spurious response rejection

This is a very interesting specification for which no clear definition seems to exist. Note definition 1.0: Spurious rejection is the ratio of a particular out of band frequency signal level required to produce a specified output to the desired signal level to produce the same output. Definition 2.0: " All superheterodyne receivers have a potential for responding to frequencies other than the desired frequency channel. This needs to be minimized by designing in spurious response rejection by proper choice of the IF frequency and use of RF filters. 70 to 100 dB is achieveable in practical receivers." Definition 3.0: Ratio of desired signal to the total of all spurious signals at an offset of channel spacing in dB. What are these spurious responses being considered? A sample of these signals is described below:
(1) Image frequency/ frequencies.
(2) Half - IF.
(3) Straight IF pickup.
(4) High order spurs result from combinations of harmonics ( m,n) which result in spurious responses so close to the desired frequency response that they cannot be filtered out.
(5) A whole family of spurious responses of type ( 1 x n) is the n x LO spurs which can be troublesome if the RF front end has return responses or re-resonances.
(6) Second image in dual conversion receivers.
(7) Spurious signals present on the LO signal itself.
(8) Transmitted signal in half duplex radios assuming the role of a LO.

These responses are difficult to measure because of signal generator wideband noise.

Nevertheless this is a key receiver specification, and needs to be understood and above all, used and specified clearly.

Impedance matching using two useful techniques

For maximum transfer of power from a source to a load, the source and load impedances must be conjugate matched. A number of techniques to do this have been developed. This post looks at two fairly simple and very popular ones. The L - section match and the cascade transmission line match. Simple analytical techniques are used to do this and described in the paper. The calculations can be done with a simple calculator. In order to access the detailed description, interested readers are directed to our website at www.signalpro.biz. Follow the links in the website to engineering pages>engineer's corner and then select the paper from the list on the page.

SFDR or Spurious free dynamic range

Someone asked a question about the significance of the SFDR. The answer to the question was as follows. ( For experienced receiver designers this is old hat of course.)

The SFDR is a specification which allows a reviewer to gauge the range of input/output signals that a receiver can handle while still in a linear range of operation.

The basic mathematical definition is:

SFDR = (2/3) x (IP3 - Noise floor)

The noise floor is defined as:

Pn(output) = kTBGF.

Where k = Boltzman's constant
T = Absolute temperature
IP3 = Third order intercept point at the output
G = Gain of the system
F = Noise factor.

Using this definition the SFDR can be calculated as:

SFDR = (2/3)(IP3 + 174 - 10logB - G - F).

Here the 174 represents the kT noise.

All quantities in dBm.

Thus if IP3 is known and gain is known , the input IP3 is known. The input signal should not exceed this as 3rd order distortion products will emerge from noise beyond this level at the input.

So an obvious conclusion is: Keep IP3 as high as possible and the noise floor as low as possible for high SFDR. Typically IP3 is about 11.6 dB above the 1 dB compression point of an amplifier.

Also it must be stressed that all components in a system, that have the potential of introducing distortion, should be assigned an IP3. Ultimately the final IP3 is the cascade of the individual IP3's.

FCC regulations for unlicensed transmitters

What does the term unlicensed transmitter actually imply? What is it that one can do with this frequency band/bands? In fact, to start a wireless system design in the unlicensed band this has to be the first step in the design. To understand this more fully we took a look at the FCC website. It is a vast website and in spite of a search engine it still takes a bit of doing to locate the relevant articles, regulations, rulings, tips etc. We did manage to locate a couple of papers which we believe are helpful for people who may want to understand this concept of the unlicensed frequency band in the US. These can be accessed through our website at www.signalpro.biz ( or, of course, through the FCC website!). Go to engineering_pages>engineer's corner and look for the unlicensed frequency band information. By the way, there are always updates to these, so it is a good idea to also check on the updates.