Noise figure (NF) is a term typically used to help quantify a receiver's sensitivity performance for RF engineers. It can be used when designing the receive system in a variety of applications, such as military software-defined radio (SDR), test and measurement equipment (including spectrum analyzers), and medical equipment. Additionally, it can help to compare the performance of individual signal chain components. In this article, we discuss NF and how it can be calculated in a single-ended-to-differential (SE-DE) fully differential amplifier (FDA), given basic circuit element values.
Many analog engineers are familiar with noise, but not necessarily NF. We begin our discussion with thermal noise, better known as white noise . This noise is due to random motion of electrons and is directly proportional to temperature.
K is Boltzman's constant (1.38 x 10–23 Joules/°K), T is temperature in K, and B is bandwidth in Hz. This noise is also independent of a given system impedance. For room temperature (290°K), we end up with –174 dBm/Hz. Any time we add an active element to a system, we impact the noise of this system beyond the thermal noise. If there is no impact on the system, the device has a noise factor of 1. This means the signal-to-noise ratio (SNR) at the input of the device is equivalent to the SNR at the device output.
thus creating Fn=1. Noise factor is dimensionless. When converted to dB, it is referred to as noise figure . The equation for NF is:
For a noise factor of 1, NF is 0 dBm. This means that there is no impairment on the system SNR. Source impedance has an impact on the system's NF. Noise power is directly proportional to the absolute temperature of the resistor.
We assume capacitors and inductors to be ideally noiseless. Therefore, only the source resistance part is to be referenced for overall noise impact. In order to have no impact on the thermal noise power, or having a system with the noise floor equal to the thermal noise kTB, the load resistance must be equivalent to the source resistance. This is another expression of the SNR ratio equation where, in a system with NF = 0 dBm,
Substituting (eNO )2 to e(NZLOAD) 2 equal load and source resistance minimally impact the system. Using Equation 5, NF is impacted when changing a component's input source resistance. When reviewing the specification of NF in datasheets, always be aware of the Rs used as reference with the NF Equation 5 in mind.
Generally, if a datasheet (for example, for an amplifier) references NF Rs=100 Ohm, while a datasheet for a similar device notes NF Rs=50 Ohms (assuming the same gain), we have an approximate 3 dB difference in NF. From this, we can assume (if input noise is not provided) that the device referencing 100 Ohms actually has lower input noise than one using 200 Ohms — if NF and gains are equal.
In our example, let's calculate NF using the LMH5401, an 8GHz low distortion, voltage feedback (VFB) FDA.
In Figure 1, we can calculate NF in a 50 Ohm system. Using Equations 7–14, we can calculate the FDA's NF:
Today we learned that, when using an SE-DE FDA, the NF has a gain of 4 V/V (12 dB) single-ended to differential. We also learned that we have an overall measured noise figure, referred to as 50 Ohms of 9.6 dB, that correlates closely with the calculated value using the provided calculations.
Join us next time, when we will discuss using active filters in clocking devices and synthesizers.
Editor's note : In writing this article, the author, Carissa Sipp, used the following as support materials: Calculating Noise Figure in Op Amps, AN-1719 Noise Figure Analysis Fully Differential Amplifier, LMH5401 datasheet, and LMH3401 datasheet.