Input referred noise

Today, I would like to discuss about "input-referred noise". Most of discussions are from Prof. Razavi's famous CMOS analog design book .

Actual (output) noise calculation can be done by killing all the input sources (i.e., voltage sources --> short and current sources --> open). This is how we can measure the noise in a laboratory. Killing all the input sources at the input terminals and putting probes at the output terminals to measure the noise. Note that the noise we can measure is "output" noise! It can never be "input".

Then, a question arises "what the heck do we want to create "input referred noise" term?".
The simple final answer is that we want to compare the noise of one circuit to the other circuit under fair comparison condition. What make input referred noise be the fair comparison measure compared to output noise? Consider the following case. Let us assume that we have two amplifiers with same noise source at the input. However, one with the gain of 1 (circuit 1) and the other with the gain of 100 (circuit 2). Now, let's measure the output noise at the output terminal. The circuit 1 has the same noise as the source noise. On the other hands, the output noise of circuit 2 becomes 100 times larger (in power quantity, 10,000 times larger) than the same noise source at the input. Can you say the 2nd circuit has larger noise than the 1st circuit? Is this fair comparison? Remember the signal also gets 100 times larger! This is one of many reasons that we would like to consider Signal-to-noise ratio (SNR), rather than only signal! One very important observation here is SNR does not depend on the gain!

In order to overcome this unfair comparsion of noise people developed a new concept called "input referred noise". The idea is to represent the effect of all noise sources in the circuit by noise sources at the input such that the output noise is equal to the output noise by simply mutliplying with gain of an amplifier.

Some important observations...

1) The input-referred noise and the input signal are both multiplied by the gain as they are processed by the circuit. Thus, the input-referred noise indicates how much the input singal is corrupted by the circuit's noise, i.e., how small an input the circuit can detect with acceptable SNR! (this input is called minimum detectable level). --> fair comparison is possible. Observing the same output SNR, what is the input SNR! Then, we can compare it with other circuit's SNR so that we can determine the noise contribution from a circuit.

2) If the circuit has a finite input impedance and is driven by a finite source impedance we have to use both voltage input noise source and current input noise source for completeness. Votlage input noise source is in series with a source and a circuit and current input noise source is in paralle with a source terminal. Let's first find when we can model sole voltage input referred noise source is sufficient. If Zs (source impedance) is zero (0), then even if input current noise source exist at the input, its current all flow through the source side. None of current from the input current noise source goes to the circuit side. Only survivor is the voltage noise source! Since the source terminal shows zero impedance and the circuit input terminal has some finite impedance, all the voltage will effectively show on the input impedance of the circuit. Conversely, if the source impedance is open (infinate impedance), all the current from the input noise source goes to the circuit! (Since a source terminal has infinite impedance, the some finite input terminal impedance of the circuit is relatively said that it has almost zero impedance in relative sense!). However, the voltage noise source all will be delivered to the source side due to its infinite impedance. THUS, to make a long story short, if a source impedance is in somewhere between 0 and infinite impedance, we have to have both voltage noise source and current noise source at the input terminal! - voltage source is in series and current source is in paralle!


Now....let's see how we can calculate the input noise !
There are two typical ways to find them. The first one is comparison method. (less often used). The other is gain divison methods.



............ INCOMPLETE!