Gain Definitions for the YFactor Method of NF Measurements: Available Gain or Insertion Gain?
The Yfactor method is a widely used technique for measuring the gain and noise figure (NF) of RF components. This article will help you understand the differences between the insertion gain and the available gain, while avoiding potentially significant errors when measuring the noise figure.
In principle, the Yfactor method is a relatively straightforward method of measuring the gain and noise figure (NF) of an RF component. However, there are some intricacies that require careful attention in practice. Several nonideal effects, such as the uncertainty of the test equipment’s NF as well as the uncertainty related to the noise source itself, can lead to measurement uncertainty. Another subtlety is that the method actually measures and uses the DUT (device under test) insertion gain rather than its available gain.
Introducing the YFactor Method
The Yfactor method for noise figure measurement consists of two steps:
 The measurement step shown in Figure 1(a) that determines the noise temperature of the DUTReceiver system denoted by T_{cas}
 The calibration step of Figure 1(b) that determines the noise temperature of the receiver T_{Receiver}
Figure 1. Two steps of Yfactor method for noise figure measurement: (a) measurement and (b) calibration
After measuring T_{cas} and T_{Receiver}, we can apply Friis’s equation to find the noise temperature of the DUT:
\[T_{cas} = T_{DUT} + \frac{T_{Receiver}}{G_{DUT}}\]
Equation 1.
where T_{DUT} and G_{DUT} denote the DUT’s noise temperature and gain, respectively. The noise powers obtained from the measurement setup (N_{h} and N_{c} in Figure 1(a)) are amplified by the DUT gain; however, N_{h,cal} and N_{c,cal} don’t experience this gain (Figure 1(b)). Therefore, G_{DUT} can be estimated by the following equation:
\[G_{DUT} = \frac{N_h  N_c}{N_{h,cal}N_{c,cal}}\]
Equation 2.
Available Power Gain
The power gain used in the noise figure definition is the available power gain,G_{A}, which is defined in the illustration of Figure 2 below. The available power gain is the ratio of the power available from the twoport network P_{AVN} (Figure 2(a)) to the power available from the source P_{AVS} (Figure 2(b)).
Figure 2. Available power gain definition
Note that for both P_{AVN} and P_{AVS} measurements, the measured port is connected to its conjugatelymatched load. For example, to find P_{AVN}, the module output is connected to the complex conjugate of Z_{out}=R_{out}+jX_{out}, i.e. Z_{L}=R_{out}jX_{out}. The power we obtain from Equation 1 is not the available power gain. To distinguish it from available gain, it is given a specific name: the insertion gain, which will be discussed below.
Insertion Power Gain
Figure 3 illustrates the definition of the insertion power gain.
Figure 3. Insertion power gain definition
The insertion power gain depends on both source and load impedances (Z_{S} and Z_{L}). As shown in Figure 3(a), we connect the DUT to Z_{L} while its input is driven by a source impedance of Z_{S}, and measure the power delivered to the load (denoted by P_{Out} in Figure 3). We also measure the power that the source can directly deliver to Z_{L}, denoted by P_{In} in Figure 3(b). The ratio of P_{Out} to P_{In} is the insertion gain of the DUT. From this explanation, it should be clear that the insertion gain corresponds to the change in power gain that we obtain when we insert the DUT between a given Z_{S} and Z_{L}.
Error Introduced by the Use of the Insertion Gain
Comparing the measurement and calibration steps of the Yfactor method (Figure 1(a) and (b)) with the insertion gain definition (Figure 3(a) and (b)), we observe that the gain we obtain from Equation 2 is actually the insertion gain rather than the available gain. It is possible to measure the DUT’s available gain; however, this requires two additional power measurements where the load impedance must be tuned to be a conjugate match to the port being measured.
The insertion gain, however, is obtained from the four power measurements required for the Yfactor method. We’re actually assuming that the insertion gain is equal to the available gain. If this is not the case, an error will be introduced in our measurements (Equation 1). It can be shown that the difference between the available gain G_{A} and insertion gain G_{i} is given by:
\[G_A (dB)  G_i (dB) = 10 log \Big ( \frac{(1\Gamma_s^2)1 \Gamma_1 \Gamma_2^2}{(1\Gamma_2^2)1 \Gamma_1 \Gamma_s^2} \Big )\]
Equation 3.
where Γ_{1} is the reflection coefficient looking into the noise measuring receiver; Γ_{2} is that observed looking into the output of the DUT; and Γ_{s} is the reflection coefficient of the noise source (Figure 4).
Figure 4. Reflection coefficients for the noise source, DUT output, and noise measuring receiver
Note that in the case of a perfect match (Γ_{1}=Γ_{2}=Γ_{s}=0), the insertion gain is equal to the available gain. In the above equation, knowledge of both the magnitude and phase of reflection coefficients is required to find G_{A} from G_{i}. Normally, the phase information is not available, and we can only find the error limits. Figure 5 shows the difference between the insertion gain and available gain as a function of match levels.
Figure 4. Ratio of available gain to insertion gain as a function of receiver and DUT matching. Image used courtesy of Anritsu.
In the above figure, the xaxis is the DUT input and output match (for simplicity, it’s assumed that the DUT’s input and output match are the same). The yaxis is the difference between the two power gains in decibels. The noise source match is assumed to be 20 dB, and the DUT is assumed to have decent isolation (S21 × S12= 0.1). Note that as the DUT match degrades beyond 10 dB, the difference between the two types of gain becomes more significant. In such cases, the gain error can introduce a significant error in the measured NF value.
SParameter Correction of Gain Error
At this point, you might wonder whether it is possible to use the S parameters of the DUT along with Equation 3 to obtain the available gain from insertion gain. By substituting G_{A} (rather than G_{i} ) into Friis’s equation, we can correct for the gain error. This appears to be of benefit, but there are two points that are worth mentioning.
First, note that we usually don’t have the phase information of the reflection coefficients (Γ_{1}, Γ_{2}, and Γ_{s}). With scalar measurements, we don’t know how the vector reflection coefficients will combine to produce the final error. Assuming that vector mismatches are available, we can find G_{A} from G_{i}.
However, there is another issue that can prevent us from having a more accurate measurement: the noise figure of the DUT and the measuring equipment is a function of their drivingpoint impedances. Figure 5 illustrates this graphically through the noise performance of a hypothetical DUT.
Figure 5. Smith Chart demonstrating impact of drivingpoint impedance on the noise figure. Image used courtesy of D. Boyd.
When the DUT is driven by a source impedance of 50 Ω (corresponding to the green circle at the center of the Smith chart), its noise figure is 2.5 dB. However, with a source impedance equal to the complex conjugate of the DUT’s S_{11} (marked by the red circle in the figure), the noise figure is 2 dB. S parameters do not provide us with any information about the noise performance of the device. Therefore, while S parameter corrections can be used to find G_{A} from G_{i}, it won’t allow us to account for the change in the DUT’s NF. Without knowledge of the NF variation with source resistance, the S parameter correction can even increase the NF measurement error.
Determining the NF dependence on the source impedance requires specialized NF measurement equipment that uses stub tuners to apply a range of complex impedances to the device. These measurements are then analyzed to produce the circular contours of NF on the Smith chart similar to that shown in Figure 5. It should be noted that common noise figure analyzers and network analyzers are not capable of producing these NF contours.
The Necessity of Specifying Measurement Uncertainty
Without having the noise contours, it is invalid to apply mismatch corrections for noise figure measurements. In these cases, it is recommended to minimize impedance mismatches of different ports as much as possible and then treat the residual mismatch as a measurement uncertainty. In addition to the mismatch effect, a complete uncertainty analysis can account for other nonideal effects, such as the uncertainty of the test equipment’s NF as well as the uncertainty related to the noise source itself. Uncertainty analysis is key in every kind of measurement, including NF measurements. The following table highlights the importance of knowing measurement uncertainty by comparing two different hypothetical amplifiers.

Noise Figure (dB) 
NF Uncertainty (dB) 
Amplifier 1 
1.2 
±0.5 
Amplifier 2 
1.4 
±0.1 
Without taking the uncertainty into account, one immediately chooses Amplifier 1 as the higherperforming device. However, considering the measurement uncertainty, we observe that Amplifier 1 can have a noise figure as large as 1.7 dB while the maximum NF of Amplifier 2 is 1.5 dB. When making noise figure measurements, a key parameter to be aware of is measurement uncertainty. In a future article, we’ll take a look at the measurement uncertainty of the Yfactor method.
YFactor Method Review
The Yfactor method actually measures and uses the DUT’s insertion gain rather than its available gain. This can lead to a significant error in the presence of impedance mismatches. Since the measurement of insertion gain is much easier than the available gain, we usually assume that these two power quantities are equal. To limit the error, however, impedance mismatches of different ports should be minimized. The residual mismatch error is usually treated as a measurement uncertainty.
Featured image used courtesy of Adobe Stock