Agilent Understanding and Improving Network Analyzer Dynamic Range Application Note 1363-1 Introduction Achieving the highest possible net- Achievable dynamic range depends work analyzer dynamic range is upon the measurement application as extremely important when character- shown in Figure 1. izing many types of microwave devices, and in some cases the key factor in determining measurement performance. To achieve the greatest P dynamic range from a network mea- max surement system, it is important to understand the essence of dynamic range and the methods that can be Receiver employed to increase it. Armed with P this knowledge, the designer can ref Dynamic choose the method that achieves the best results with the least impact on Range other instrument parameters such as System measurement speed. Dynamic Network analyzer dynamic range is Range essentially the range of power that the system can measure, specifically: P •Pmax: The highest input power min level that the system can measure before unacceptable errors occur Figure 1. in the measurement, usually determined by the network • System dynamic range: The analyzer receiver's compression dynamic range that can be specification. realized without amplification •Pref: The nominal power available such as when measuring passive at the test port from the network components such as attenuators analyzer's source. and filters. •Pmin : The minimum input power level the system can measure (its • Receiver dynamic range: The sensitivity), set by the receiver's system’s true dynamic range if it is noise floor. Pmin depends on the considered a receiver. An amplifi- IF bandwidth, averaging, and the er may be required to realize the test set configuration. receiver’s full dynamic range. This can be the device under test or an The two common definitions for external amplifier added to the dynamic range are: measurement system. • Receiver dynamic range = Pmax – Pmin • System dynamic range = Pref – Pmin 2 Noise floor defined The receiver's noise floor is an impor- Agilent’s new PNA series vector net- tant network analyzer specification work analyzers use the RMS value to that helps determine its dynamic define receiver noise floor. This is a range. Unfortunately, “noise floor” is commonly used definition, and is not a well-defined term and it has easy to understand because it is the been defined several ways over the receiver's equivalent input noise years. power. The results of an experiment to com- pare some common noise floor defini- tions are shown in Figure 2. In this experiment, Gaussian random noise with a noise power of –100 dBm was simulated, and the noise floor was calculated using four definitions: • The solid line shows the RMS value of the noise, which is equal to the noise power of –100 dBm. • The dashed line (–101 dBm) is the mean value of the linear magni- tude of the noise, converted to dBm. • The dotted line (–102.4 dBm) is the mean value of the log magni- tude of the noise. • The dot-dash line (–92.8 dBm) is the sum of the mean value of the linear magnitude of the noise and three times its standard deviation, Figure 2. Various noise floor definitions converted to dBm. Improving dynamic range In some measurement situations, it is desirable to increase the network ana- lyzer’s dynamic range beyond the level obtained with the default settings. Noise floor sets the minimum power level that the instrument can measure and thus limits its dynamic range. Noise floor can be improved by using averaging, or by reducing the system bandwidth (IF BW). Smoothing is another technique that is often considered to be akin to averag- ing and IF BW adjustment, but it does not reduce the noise floor. Smoothing is adjacent-point averaging of the for- matted data, similar to video filtering. Trace-to-trace (or sweep-to-sweep) averaging operates on the pre-format- ted, vector data, so that it can actually reduce the noise power. This key dif- ference is responsible for the inability of smoothing to reduce noise floor, although it does reduce small peak-to- peak variations of noise on a trace.1 3 Averaging IF BW reduction and exhibits a Gaussian probability The PNA Series and many other net- The IF BW of the system can be distribution (which can be proved by work analyzers perform sweep-to- altered via the front panel or remote the central limit theorem3). sweep averaging by taking an expo- programming, and its value will affect nentially weighted average of the data the digital filtering that is performed A high level of confidence in the rela- points from each sweep. Exponen- on the data collected in the analyzer’s tionship between noise floor and IF tially weighting the samples in the receivers. Decreasing IF BW will BW makes it possible to precisely cal- data set allows averaging to proceed reduce noise floor by filtering out culate the noise floor reduction without termination, even after the noise that is outside the bandwidth of achieved by decreasing the IF BW. An desired averaging factor has been the digital filter. empirical study was performed using reached. The averaging is performed the PNA network analyzer in which on complex data, which means that The low level noise that is present in the RMS noise level was measured at the data is averaged vectorially. the analyzer’s receiver chain is caused 5 different CW frequencies (1, 3, 5, 7, by thermal noise arising from the and 9 GHz). There were 801 points in Many signal analyzers use scalar aver- thermal agitation of electrons in resis- the sweep and the IF BW was set to 1 aging, which mitigates only the vari- tances. Consequently, it is directly Hz, 10 Hz, 100 Hz, 1 kHz, and 10 kHz. ance of the noise but does not affect proportional to bandwidth. The mean- The noise floor of the VNA was mea- the average noise level. When a trace square value of the thermal noise sured with no signal present at the that contains both coherent signal voltage is given by: test ports. In Figure 3, the observed and uncorrelated noise is averaged in relationship between the noise floor the vector sense, the noise compo- E 2 = 4RkTB and the IF BW shows that the PNA’s nent will approach zero, and the RMS noise floor very closely follows resulting trace will show the desired where the theoretical expectation. Deviation signal with less noise present. When k is Boltzmann's constant from theory is negligible. viewed with the log magnitude format (1.38 e-23 joules/Kelvin) on the network analyzer display, it T is the absolute temperature in As with averaging, decreasing IF BW becomes clear that the average noise degrees Kelvin to reduce noise floor reduces mea- level is reduced and an improvement R is the resistive component in surement speed. While it could be in dynamic range is achieved. ohms expected that a factor-of-10 decrease B is the bandwidth in Hertz in IF BW will reduce the noise floor Using the averaging function available by 10 dB and will cause a factor-of-10 in most vector network analyzers, sig- The noise power delivered to a com- increase in measurement time, this is nal-to-noise ratio is improved by 3 dB plex conjugate load is not always true because the digital fil- for every factor-of-2 increase in aver- ters used in a network analyzer at dif- ages. This is a powerful method for Pn = E 2 = kTB ferent IF bandwidths may vary in reducing noise floor. However, it also 4R shape. In the PNA Series for example, reduces measurement speed because sweep time increases by a factor that when two traces must be averaged, This is the familiar ‘kTB’ relationship is less than 10 for a factor-of-10 measurement time doubles. for noise power2. reduction in IF BW. This means that to achieve the same reduction in Averaging can only be used on ratioed Noise is random in nature and is con- noise floor, IF BW reduction will measurements, and will not work on sidered nondeterministic because it is reduce measurement speed less than measurements using a single receiver caused by a collection of small events will averaging. channel. Averaging is not allowed on unratioed measurements because phase is random in this mode and averaging (which is performed in the complex domain), will always cause the result to approach zero. Figure 3. RMS noise floor vs IF BW (n=801 pts) 4 Choosing the best method There are other factors that can be considered when deciding which To achieve noise floor reduction, This example uses a fairly fast IF BW, method to choose for increasing averaging can be increased or IF BW and shows that IF BW reduction pro- dynamic range in a given measure- reduced. If measurement speed is not duces a benefit over averaging when ment application. Using averaging to of paramount concern, either method attempting to improve dynamic range. reduce noise floor allows the user to will work equally well. The time However, now consider a slower observe the traces on the PNA screen required to acquire and process data sweep mode (i.e., lower IF BW). If the as the averaging progresses, which for a trace (called cycle time), PNA is set at an IF BW of 100 Hz and some designers may find useful. IF includes not only sweep time, but a noise floor reduction of 10 dB is BW reduction works on both ratioed also retrace time, band-crossing time, desired, averaging with a factor of 10 and unratioed measurements (unlike and display update time.