How to improve the dynamic range of a network analyzer?

When characterizing many types of microwave devices, achieving the highest possible network analyzer dynamic range is extremely important and, in some cases, a critical factor in determining measurement performance. To obtain the maximum dynamic range from a network measurement system, it is important to understand the nature of dynamic range and what methods can be used to increase it. With this knowledge, designers can choose the appropriate method to achieve the best results and minimize the impact on other parameters, such as measurement speed.

Defining Dynamic Range

The dynamic range of a network analyzer is essentially the range of powers that the system can measure:

–Pmax: Indicates the highest input power level that can be measured before unacceptable errors occur in the system during the measurement process. It is usually determined by the compression technical specifications of the network analyzer receiver.

–Pref: represents the nominal power at the test port from the network analyzer signal source.

– Pminimum: represents the minimum input power level that the system can measure (its sensitivity), which depends on the noise floor of the receiver. Pminimum depends on the IF bandwidth, averaging, and test configuration.

Two commonly used definitions of dynamic range are:

– Receiver dynamic range = Pmax – Pmin

–System dynamic range = Preference value – Pminimum value

Figure 1. Dynamic range definition.

The achievable dynamic range depends on the measurement application, as shown in Figure 1.

– System dynamic range: The dynamic range that can be achieved without amplification, such as when measuring passive components such as attenuators and filters.

– Receiver dynamic range: If you think of the receiver as a system, then this is the true dynamic range of the system. To achieve the full dynamic range of the receiver, an amplifier may be needed. This can be the device under test or an external amplifier added to the measurement system.

Noise Floor Definition

The receiver noise floor is an important network analyzer specification that helps determine the receiver dynamic range. Unfortunately, "noise floor" is not a well-defined term and has been defined in many different ways over the years.

Figure 2. Various noise floor definitions

Figure 2 shows some common definitions of background noise through experiments. In this experiment, we simulated Gaussian random noise with a noise power of -100dBm and calculated it using four definitions:

– The solid line in the figure represents the RMS value of noise, which is equal to -100dBm noise power.

– The dashed line (-101dBm) is the average of the linear amplitude of the noise, converted to dBm.

– The dotted line (-102.4dBm) is the average value of the logarithmic magnitude of the noise.

– The dash-dot line (-92.8 dBm) is the sum of the mean of the noise linear amplitude and three times its standard deviation, converted to dBm.

Keysight's vector network analyzers (VNAs), such as the PNA network analyzer or ENA network analyzer series, define the receiver noise floor using an RMS value. This is a common definition that is easy to understand because it is the equivalent input noise power of the receiver.

Improve dynamic range

In some measurement situations it is necessary to increase the dynamic range of a network analyzer beyond the levels obtained using the default settings. The noise floor determines the minimum power level that the instrument can measure, thus limiting its dynamic range. The noise floor can be improved by using averaging or by reducing the system IF bandwidth (IFBW).

Smoothing is another technique that is often thought of as similar to averaging and IFBW adjustment, but it does not reduce the noise floor. Smoothing is an averaging of neighboring points in formatted data, similar to video filtering. When averaging trace to trace (or scan to scan), it is done on pre-formatted vector data, so it actually reduces noise power. This key difference results in the inability to reduce the noise floor when smoothing, although it does reduce small variations in peak-to-peak noise across a trace.

average value

Keysight's VNAs and many other network analyzers perform sweep-to-sweep averaging by exponentially weighted averaging of the data points within each sweep. Exponentially weighting the samples within a data set allows averaging to proceed without terminating even after the desired averaging factor has been reached. Averaging complex data simply means that the data is vector averaged.

Many signal analyzers use scalar averaging, which only reduces the variance of the noise and does not affect the average noise level. When averaging in a vector sense, if a trace contains both coherent signal and uncorrelated noise, the noise component will approach zero and the resulting trace will show the desired signal with less noise. When viewed in logarithmic magnitude format on a network analyzer display, it is clear that the average noise level is reduced and the dynamic range is improved.

Using the averaging function available in most vector network analyzers, the signal-to-noise ratio improves by 3dB for every factor of 2 increase in averaging. This is an effective way to lower the noise floor. However, it also slows down the measurement because the measurement time doubles when two traces must be averaged.

Averaging is only possible for ratiometric measurements and not for measurements made with a single receiver channel. Non-ratiometric measurements do not allow averaging because the phase is random in this mode and averaging (performed in the complex domain) will always result in a result close to zero.

Reduce IF bandwidth

The system's IF bandwidth can be changed via the front panel or remote programming, and its value will affect the digital filtering performed on the data collected in the analyzer receiver. Reducing the IF bandwidth will filter out noise outside the digital filter bandwidth, thereby lowering the noise floor.

The low-level noise in the analyzer receiver chain is caused by thermal noise caused by the thermal agitation of the resistor electrons. It is therefore proportional to the bandwidth. The mean square value of the thermal noise voltage is given by:

in

k is the Boltzmann constant (1.38e-23 joules/Kelvin)

T is the absolute temperature in Kelvin

R is the resistance component in ohms

B is the bandwidth in Hertz

The noise power delivered to the complex conjugate load is

This is known as the noise power “kTB” relationship2.

Noise is random in nature and is considered nondeterministic because it is caused by a collection of small events, exhibiting a Gaussian probability distribution (as can be proved by the central limit theorem3).

Figure 3. RMS noise floor vs. IF bandwidth (n=801pts)

The high confidence in the relationship between the noise floor and IF bandwidth allows for accurate calculation of noise floor reduction by reducing the IF bandwidth. An empirical study was conducted using a Keysight Technologies PNA network analyzer where the RMS noise level was measured at 5 different CW frequencies (1, 3, 5, 7, and 9 GHz). There were 801 points in the sweep with the IF bandwidth set to 1 Hz, 10 Hz, 100 Hz, 1 kHz, and 10 kHz. The noise floor of the PNA was measured with no signal at the test port. In Figure 3, the observed relationship between the noise floor and the IF bandwidth shows that the RMS noise floor of the PNA is very close to the theoretical expectation. The deviation from the theoretical value is negligible.

As with averaging, reducing the noise floor by reducing the IF bandwidth will also slow down the measurement. While you might expect that reducing the IF bandwidth by a factor of 10 will reduce the noise floor by 10dB while increasing the measurement time by a factor of 10, this is not always true because the shape of the network analyzer digital filter may be different at different IF bandwidths. For example, for Keysight’s VNAs, reducing the IF bandwidth by a factor of 10 increases the sweep time by less than a factor of 10. This means that to achieve the same noise floor reduction, reducing the IF bandwidth has less of an impact on measurement speed than averaging.

Choosing the best method

To reduce the noise floor, either increase the averaging or reduce the IF bandwidth. If measurement speed is not the most important consideration, either approach is equally effective. The time required to acquire and process the trace data (called the cycle time) includes not only the sweep time, but also the retrace time, band crossing time, and display update time.

Since averaging requires multiple traces and updating the display each time, averaging generally takes longer to perform than reducing the IF bandwidth, especially if multiple averages are required. Keep in mind that most of the differences affecting measurement time are caused by the digital filtering performed on the various IF bandwidths. This effect is reflected in the sweep time component of the cycle time, so to determine the impact of the two noise reduction methods on measurement time, it is appropriate to consider only the sweep time.

Take the PNA series with 10kHz IF bandwidth as an example. If a 10dB improvement in dynamic range is required, it can be achieved by averaging 10 sweeps or setting the IF bandwidth to 1kHz. Table 1 shows the impact on sweep time of the two methods used to improve the dynamic range by 10 or 20dB.

This example uses a fairly fast IF bandwidth and shows that reducing the IF bandwidth can have advantages over averaging when trying to improve dynamic range. However, now consider a slower sweep mode (i.e., lower IF bandwidth). If the PNA is set to a 100Hz IF bandwidth and a 10dB reduction in the noise floor is desired, 10 averages can be applied, or the IF bandwidth can be reduced to 10Hz. Table 2 shows the effect on sweep time.

The increase in cycle time is closely related to the increase in sweep time. If the network analyzer is in fast sweep mode, the improvement in dynamic range obtained by reducing the IF bandwidth has a significantly better impact on measurement speed than performing averaging. For slow sweep mode, both methods have roughly the same impact on measurement speed.