# System Noise-Figure Analysis for Modern Radio Receivers

Abstract: Noise figure is routinely used by system and design engineers to ensure optimal signal performance. However, the use of mixers in the signal chain creates challenges with straightforward noise-figure analysis. This tutorial starts by examining the fundamental definition of noise figure and continues with an equation-based analysis of cascade blocks involving mixers, followed by typical lab techniques for measuring noise figure. This tutorial also covers the concepts of noise temperature and Y-factor noise measurement before exploring the use of the Y-factor method for mixer noise-figure measurements. Examples of double-sideband (DSB) and single-sideband (SSB) noise-figure measurements are discussed.

*Microwave Journal*.

## Introduction

_{OUT}= |f

_{RF}- f

_{LO}|. In heterodyne architectures, one of these contributions is typically considered spurious and the other intended. Therefore, image reject filtering or image canceling schemes are likely to be employed to largely remove one of these responses. In direct-conversion receivers, the case is different; both sidebands (above and below f

_{RF}= f

_{LO}) are converted and utilized for the wanted signal. Consequently, this is truly a double-sideband (DSB) application of the mixers.

_{SSB}, assumes that the noise from both sidebands is allowed to fold into the output signal. However, only one of the sidebands is useful for conveying the wanted signal. This naturally results in a 3dB increase in noise figure, assuming that the conversion gain at both responses is equal. Conversely, the DSB noise figure assumes that both responses of the mixer contain parts of the wanted signal and, therefore, noise folding (along with corresponding signal folding) does not impact the noise figure. The DSB noise figure finds application in direct-conversion receivers as well as in radio astronomy receivers. However, deeper analysis shows that it is not sufficient for designers just to choose the right “flavor” of noise figure for a given application and then to substitute the corresponding number in the standard Friis equation. Doing so can lead to substantially faulty analysis, which could be particularly severe in cases when the mixers or components following the mixer play a non-negligible role in determining system noise figure.

## Conceptual Model of Mixer Noise

**Figure 1**). This model is based on one provided by Agilent’s Genesys simulation program.

^{1}

*Figure 1. Mixer noise contributions.*

_{A}, representing the total additional noise power per unit bandwidth available from the mixer output port.

N_{A} = N_{S}G_{S} + N_{I}G_{I} + N_{IF} |
(Eq. 1) |

_{A}is not at all dependent on the presence or absence of signals at the mixer’s input port.

**Figure 2**). We identified two discrete noise sources representing the input noise density due to the source termination at the wanted frequency and the image frequency, respectively. We must account for these as independent quantities, because the application circuit can cause one of them to be attenuated and the other transferred with low loss to the mixer’s RF input port. This will likely be the case, if the image and wanted RF frequencies are well separated and a frequency-selective match is employed.

*Figure 2. Source noise and mixer noise contributions.*

_{OUT}= N

_{A}+ kT

_{0}G

_{S}+ kT

_{0}G

_{I}. However, in the case of a high-Q, frequency-selective match to the mixer at the wanted RF frequency, the noise at the output due to the source termination at the image frequency is likely to be negligible, leading to N

_{OUT}= N

_{A}+ kT

_{0}G

_{S}. Generally, we can assign a coefficient, α, to the effective fraction of the input source-termination noise power available to the mixer’s input port at the image frequency. Thus, N

_{OUT}= N

_{A}+ kT

_{0}G

_{S}+ αkT

_{0}G

_{I}, where α is an application-specific coefficient in the range 0 ≤ α ≤ 1. Later we shall see that the effective noise figure in an application depends on the value of α.

## Noise-Figure Definitions

F = (SNR_{IN})/(SNR_{OUT}) |
(Eq. 2) |

NF = 10log_{10}(F) |
(Eq. 3) |

_{IN}and the signal gain be G

_{s}. Then, the output power is given by P

_{OUT}= G

_{s}P

_{IN}and:

(Eq. 4) |

_{IN}and N

_{OUT}, are ill-defined unless we specify the bandwidths in which they are measured. This can be solved by specifying N

_{IN}and N

_{OUT}to represent noise power per unit bandwidth at any given specified input and output frequency.

### Single-Sideband Noise Factor

^{®}definition of noise factor:

**Noise Factor (Noise Figure) (of a Two-Port Transducer).**At a specified input frequency the ratio of 1) the total noise power per unit bandwidth at a corresponding output frequency available at the output

*Port*to 2) that portion of 1) engendered at the input frequency by the input termination at the

*Standard Noise Temperature*(290K).

*Note 1*: For heterodyne systems there will be, in principle, more than one output frequency corresponding to a single input frequency, and vice versa; for each pair of corresponding frequencies a

*Noise Factor*is defined.

*Note 2*: The phrase “available at the output

*Port*" may be replaced by “delivered by the system into an output termination."

*Note 3*: To characterize a system by a

*Noise Factor*is meaningful only when the input termination is specified.

^{2}

**Figure 3**).

*Figure 3. SSB noise figure.*

*total*noise power per unit bandwidth at a corresponding output frequency without making any specific exclusions. To make this explicit in mathematical form for the case of a mixer with signal and image responses, the above definition can be written as:

(Eq. 5) |

_{I}is the conversion gain at the image frequency; G

_{S}is the conversion gain at the signal frequency; T

_{0}is the standard noise temperature; and N

_{A}is the noise power per unit bandwidth added by the mixer’s electronics as measured at the output terminals. The corresponding noise factor for the image frequency can be written as:

(Eq. 6) |

*Port*.”

^{3}They therefore assume:

(Eq. 7) |

**Figure 4**.

*Figure 4. IEEE variant of SSB noise figure.*

**Noise figure (NF):**The ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature (usually 290K).

*Note*: The noise figure is thus the ratio of actual output noise to that which would remain if the device itself did not introduce noise. In heterodyne systems, output noise power includes spurious contributions from image-frequency transformation, but the portion attributable to thermal noise in the input termination at standard noise temperature includes only that which appears in the output via the principal frequency transformation of the system, and excludes that which appears via the image frequency transformation.

*Synonym*

**noise factor**.

^{4}

(Eq. 8) |

_{S}= G

_{I}. Then:

(Eq. 9) |

_{A}= 0, then we are left with F = 2 or NF = 3.01dB. This corresponds to the statement that the SSB noise figure of a noiseless mixer is 3dB.

### Double-Sideband Noise Factor

**Figure 5**illustrates this case.

*Figure 5. DSB noise figure.*

(Eq. 10) |

_{s}= G

_{i}, then:

F_{DSB} = 1 + (N_{A}/(2kT_{0}G_{S})) |
(Eq. 11) |

F_{SSB} = 2 + N_{A}/(kT_{0}G_{S}) |
(Eq. 12) |

_{A}= 0), then F

_{DSB}= 1 or NF

_{DSB}= 0dB.

## Use of Noise Figures in Cascaded Noise-Figure Calculations

### Baseline Case: Cascade of Linear Circuit Blocks

**Figure 6**).

*Figure 6. Three gain blocks cascaded.*

N_{OUT} = kT_{0}G_{1}G_{2}G_{3} + N_{A}1 G_{2}G_{3} + N_{A2}G_{3} + N_{A3} |
(Eq. 13) |

N_{OT} = kT_{0}G_{1}G_{2}G_{3} |
(Eq. 14) |

(Eq. 15) |

(Eq. 16) |

(Eq. 17) |

### A Heterodyne Conversion Stage

**Figure 7**). The DSB noise figure of the mixer is 3dB and its conversion gain is 10dB. The wanted carrier frequency is at 2000MHz and the LO is chosen at 1998MHz, so that both the wanted and image frequencies are within the passband of the filter.

*Figure 7. Heterodyne stage with no image rejection.*

**Table 1**, where CF is the channel frequency, CNP is the channel noise power (measured in 1MHz bandwidth), gain is the stage gain, CG is the cascaded gain up to and including the present stage, and CNF is the cascaded noise figure.

Table 1. Simulated Cascaded Performance* | |||||

Parts | CF (MHz) | CNP (dBm) | Gain (dB) | CG (dB) | CNF (dB) |

CWSource_1 | 2000 | -113.975 | 0 | 0 | 0 |

BPF_Butter_1 | 2000 | -113.975 | -7.12E-04 | -7.12E-04 | 6.95E-04 |

BasicMixer_1 | 2 | -97.965 | 10 | 9.999 | 6.011 |

**Figure 8**). At this value of the LO frequency, the image is at 1500MHz, which is well outside the passband of the filter in front of the mixer.

*Figure 8. Heterodyne stage with image rejection.*

**Table 2**. The gain of the wanted signal is the same as before, but the cascaded noise figure (CNF) has changed to a value of 4.758dB.

Table 2. Simulated Cascaded Performance* | |||||

Parts | CF (MHz) | CNP (dBm) | Gain (dB) | CG (dB) | CNF (dB) |

CWSource_1 | 2000 | -113.975 | 0 | 0 | 0 |

BPF_Butter_1 | 2000 | -113.975 | -7.12E-04 | -7.12E-04 | 6.95E-04 |

BasicMixer_1 | 250 | -99.218 | 10 | 9.999 | 4.758 |

(Eq. 18) |

N_{A} = 2kT_{0}G_{S}(10^{(3/10)} - 1) |
(Eq. 19) |

_{OUT}= N

_{A}+ kT

_{0}G

_{S}+ αkT

_{0}G

_{I}, with α = 0 in this application. Thus:

N_{OUT} = 2kT_{0}G_{S}(10(3/10) - 1) + kT_{0}G_{S} |
(Eq. 20) |

(Eq. 21) |

NF = 10log_{10}(2(10^{(3/10)} - 1) + 1) = 4.757dB |
(Eq. 22) |

F_{SSBe} = 2(F_{DSB} – 1) + 1 + α |
(Eq. 23) |

_{SSBe}= 2F

_{DSB}, which is the case illustrated at the beginning of this section. In some scenarios, fractional values of a can arise, e.g., if the image suppression filter is not directly coupled to the mixer input terminals or if the frequency separation between image and wanted responses is not large.

### A Heterodyne Receiver

**Figure 9**. To calculate the cascaded noise figure of the entire chain, we need to encapsulate the mixer and its associated LO and image reject filtering as an equivalent two-port network that has specific gain and noise figure. The effective noise factor of this two-port network is F

_{SSBe}= 2(F

_{DSB}– 1) + 1, since the termination noise at the image frequency is well suppressed by the preceeding filter.

*Figure 9. Heterodyne mixer in the context of adjacent system blocks.*

**Table 3**. Manual calculations show that this result is consistent with the standard Friis equation using 4.757dB for the mixer noise figure.

Table 3. Simulated Cascaded Performance of Heterodyne Mixer in a System | ||||||

Parts | CF (MHz) | CNP (dBm) | Gain (dB) | SNF (dB) | CG (dB) | CNF (dB) |

CWSource_1 | 2000 | -113.975 | 0 | 0 | 0 | 0 |

Lin_1 | 2000 | -100.975 | 10 | 3 | 10 | 3 |

BPF_Butter_1 | 2000 | -100.976 | -7.12E-04 | 7.12E-04 | 9.999 | 3 |

BasicMixer_1 | 250 | -90.563 | 10 | 3 | 19.999 | 3.413 |

Lin_2 | 250 | -61.695 | 25 | 25 | 44.999 | 7.281 |

### A Zero-IF Receiver

**Figure 10**).

More detailed image (PDF, 291kB)

*Figure 10. ZIF receiver with a low-noise amplifier (LNA), mixers, filters, and variable-gain amplifiers (VGAs).*

**Table 4**, where CP is channel power and SNF is stage noise figure. The other items are the same as in previous tables.

Table 4. ZIF Receiver Lineup | |||||||

Parts | CF (MHz) | CP (dBm) | CNP (dBm) | Gain (dB) | SNF (dB) | CG (dB) | CNF (dB) |

MultiSource_1 | 950 | -79.999 | -116.194 | 0 | 0 | 0 | 0 |

FE_BPF | 950 | -80.009 | -116.194 | -9.99E-03 | 1.00E-02 | -9.99E-03 | 9.99E-03 |

Lin_1 | 950 | -70.008 | -103.194 | 10 | 3 | 9.99 | 3.01 |

Split2_1 | 950 | -73.018 | -105.992 | -3.01 | 3.01 | 6.98 | 3.222 |

BasicMixer_1 | 0 | -67.039 | -99.425 | 5.979 | 4 | 12.959 | 3.81 |

LPF1 | 0 | -67.04 | -99.425 | -8.23E-04 | 1.00E-02 | 12.958 | 3.81 |

Lin_2 | 0 | -57.036 | -83.078 | 9.995 | 25 | 22.953 | 10.163 |

LPF2 | 0 | -57.038 | -83.08 | -1.90E-03 | 1.00E-02 | 22.951 | 10.163 |

**Table 5**we show the results of calculations using the conventional Friis formula for cascaded noise figure. The main difference with Table 4, which shows results from a simulator, is in the final column, CNF.

Table 5. Friis Cascade Equation Results | ||||

Parts | F (dB) | Gain (dB) | CG (dB) | CNF (dB) |

BPF filter | 0.01 | -0.01 | -0.01 | 0.01 |

LNA | 3 | 10 | 9.99 | 3.01 |

Splitter | 3.01 | -3.01 | 6.98 | 3.22 |

Mixer | 4 | 5.979 | 12.96 | 3.81 |

LPF1 | 0.01 | -0.01 | 12.95 | 3.81 |

VGA | 25 | 9.995 | 22.94 | 12.65 |

LPF2 | 0.01 | -0.01 | 22.93 | 12.65 |

**Figure 11**).

*Figure 11. Cascade including a mixer.*

N_{OUT} = 2kT_{0}G_{1}G_{2}G_{3} + 2N_{A1}G_{2}G_{3} + N_{A}2G_{3} + N_{A3} |
(Eq. 24) |

N_{OT} = 2kT_{0}G_{1}G_{2}G_{3} |
(Eq. 25) |

(Eq. 26) |

F_{1} = 1 + N_{A1}/(kT_{0}G_{1}), F_{2DSB} = 1 + N_{A2}/(2kT_{0}G_{2}), and F_{3} = 1 + N_{A3}/(kT_{0}G_{3}) |
(Eq. 27) |

F_{DSB} = F_{1} + (F_{2DSB} - 1)/G_{1} + (F_{3} - 1)/(2G_{1}G_{2}) |
(Eq. 28) |

**Table 6**.

Table 6. DSB Cascade Equation Results | ||||

Parts | F (dB) | Gain (dB) | CG (dB) | CNF (dB) |

BPF filter | 0.01 | -0.01 | -0.01 | 0.01 |

LNA | 3 | 10 | 9.99 | 3.01 |

Splitter | 3.01 | -3.01 | 6.98 | 3.22 |

Mixer | 4 | 5.979 | 12.96 | 3.81 |

LPF1 | 0.01 | -0.01 | 12.95 | 3.81 |

VGA | 25 | 9.995 | 22.94 | 10.17 |

LPF2 | 0.01 | -0.01 | 22.93 | 10.17 |

**Table 7**.

Table 7. LIF Receiver Simulation Results | |||||||

Parts | CF (MHz) | CP (dBm) | CNP (dBm) | Gain (dB) | SNF (dB) | CG (dB) | CNF (dB) |

MultiSource_1 | 950.3 | -79.999 | -116.194 | 0 | 0 | 0 | 0 |

FE_BPF | 950.3 | -80.009 | -116.194 | -9.99E-03 | 1.00E-02 | -9.99E-03 | 9.99E-03 |

Lin_1 | 950.3 | -70.008 | -103.194 | 10 | 3 | 9.99 | 3.01 |

Split2_1 | 950.3 | -73.018 | -105.992 | -3.01 | 3.01 | 6.98 | 3.222 |

BasicMixer_1 | 0.3 | -67.067 | -96.335 | 5.938 | 4 | 12.918 | 6.94 |

LPF1 | 0.3 | -68.467 | -96.458 | -1.64E-03 | 1.00E-02 | 12.916 | 6.819 |

Lin_2 | 0.3 | -58.832 | -80.068 | 9.969 | 25 | 22.885 | 13.241 |

LPF2 | 0.3 | -58.483 | -80.072 | -4.68E-03 | 1.00E-02 | 22.88 | 13.241 |

N_{OT} = kT_{0}G_{1}G_{2}G_{3} |
(Eq. 29) |

(Eq. 30) |

(Eq. 31) |

(Eq. 32) |

**Figure 12**and the corresponding results are tabulated in

**Table 8**.

Table 8. LIF Receiver Image Rejection Simulation Results | |||||||

Parts | CF (MHz) | CP (dBm) | CNP (dBm) | Gain (dB) | SNF (dB) | CG (dB) | CNF (dB) |

MultiSource_1 | 950.3 | -79.995 | -116.194 | 0 | 0 | 0 | 0 |

FE_BPF | 950.3 | -80.005 | -116.194 | -9.99E-03 | 1.00E-02 | -9.99E-03 | 9.99E-03 |

Lin_1 | 950.3 | -70.004 | -103.194 | 10 | 3 | 9.99 | 3.01 |

Split2_1 | 950.3 | -73.014 | -105.992 | -3.01 | 3.01 | 6.98 | 3.222 |

BasicMixer_1 | 0.3 | -67.053 | -96.441 | 5.958 | 4 | 12.938 | 6.815 |

LPF1 | 0.3 | -67.055 | -96.443 | -1.64E-03 | 1.00E-02 | 12.936 | 6.815 |

Lin_2 | 0.3 | -57.047 | -80.09 | 9.991 | 25 | 22.927 | 13.177 |

LPF2 | 0.3 | -57.051 | -80.094 | -3.82E-03 | 1.00E-02 | 22.923 | 13.177 |

Split290_2 | 0.3 | -54.062 | -80.145 | 3.001 | 3.02 | 25.923 | 10.125 |

^{®}Genesys to simulate these architectures and scenarios has proven to agree with mathematical derivations of the appropriate cascaded noise figure in the cases examined.

**Table 9**.

Table 9. Summary of Derived Equations | ||

Structure | Application | Cascaded F Equation |

Three gain blocks | Any | |

Heterodyne mixer | SSB, ideal image filtering | |

Complex downconverter | ZIF | |

Complex downconverter | LIF, no image suppression | |

Complex downconverter | LIF, image reject combining |

## Noise Temperature

_{e}, by F = 1 + T

_{e}/T

_{0}, where T

_{0}is defined as the reference noise temperature of 290K. Unsurprisingly, a noise factor of 1 is represented by an equivalent noise temperature of the device of 0K, whereas a noise factor of 2 is represented by T

_{e}= 290K.

## Y-Factor

^{5}involves the use of a calibrated noise source, which has two distinct noise temperatures depending on the presence or absence of DC power to the device. The calibrated source has a characterized excess noise ratio (ENR) defined as:

ENR_{dB} = 10log_{10} [(T_{S}^{ON} - T_{S}^{OFF})/T_{0}] |
(Eq. 33) |

_{S}

^{ON}is the noise temperature of the source in its ON state and T

_{S}

^{OFF}is the corresponding value in its OFF state. The Y-factor is a ratio of two noise power levels, one measured with the noise source ON and the other with the noise source OFF.

Y = N^{ON}/N^{OFF} |
(Eq. 34) |

Y = T^{ON}/T^{OFF} |
(Eq. 35) |

## Noise-Factor Measurement and Calculation

_{1}and the instrument have a noise temperature T

_{2}. While it is impossible to eliminate the measurement device’s noise temperature (T

_{2}) from any given reading, we can measure T

_{12}, which is the combined noise temperature of the DUT followed by the instrument. We can use calculations to isolate T

_{1}since T

_{12}= T

_{1}+ T

_{2}/G

_{1}. So, the strategy is to take a Y-factor measurement with the calibrated noise source connected directly to the measuring instrument, which will allow T

_{2}to be determined. We have:

Y_{2} = N_{2}^{ON}/N_{2}^{OFF} = (T_{S}^{ON} + T_{2})/(T_{S}^{OFF} + T_{2}) |
(Eq. 36) |

(Eq. 37) |

_{S}

^{ON}and T

_{S}

^{OFF}, the next step is to measure a new Y-factor for the cascade of the DUT and the measuring instrument:

Y_{12} = N_{12}^{ON}/N_{12}^{OFF} |
(Eq. 38) |

T_{12} = (T_{S}^{ON} - Y_{12} T_{S}^{OFF})/(Y_{12} - 1) |
(Eq. 39) |

_{1}

^{ON}and N

_{1}

^{OFF}and now having access to N

_{12}

^{ON}and N

_{12}

^{OFF}, we have sufficient information to calculate the gain of the DUT as:

G_{1}= (N_{12}^{ON} - N_{12}^{OFF})/(N_{2}^{ON} - N_{2}^{OFF}) |
(Eq. 40) |

T_{1} = T_{12} - T_{2}/G_{1} |
(Eq. 41) |

### Losses Before the DUT

_{1}

^{IN}. Assuming that these losses are absorbative, the following equation can be used:

T_{1}^{IN} = (T_{1}/L^{IN}) - ((L^{IN} - 1)T_{L}/L^{IN}) |
(Eq. 42) |

_{L}is the physical temperature of the loss and L

^{IN}is the insertion loss to be compensated, which is expressed as a linear power ratio greater than unity.

## Mixer as DUT in the Y-Factor Noise-Factor Determination

### Example of the DSB Noise-Figure Measurement by the Y-Factor Method

**Figure 13**). The only data collected by the simulation (

**Tables 10**and

**11**) are the channel noise power in 100kHz bandwidth both at the input (directly connected to the noise source in lieu of a calibration step) and at the output (representing the measurement mode).

*Figure 13. Simulation schematic to determine the DSB mixer noise figure using the Y-factor method.*

Table 10. Y-Factor Simulation Results for the DSB Mixer Measurement | |||||

B (Hz) | IL (dB)* | pinOFF (dBm) | pinON (dBm) | poutOFF (dBm) | poutON (dBm) |

100,000 | 0 | -123.975 | -109 | -107.265 | -96.91 |

Table 11. Y-Factor Calculations for the DSB Mixer Measurement | |||||||

Y_{2} |
Y_{12} |
T_{12} (K) |
T_{2} (K) |
T_{1} (K) |
T_{1}^{IN} (K) |
F (dB) | G (dB) |

31.443 | 10.851 | 606.147 | 0 | 606.147 | 606.147 | 4.9 | 8.8 |

_{2}represents the noise temperature of the instrument, which is acceptable, since the instrument is, in this case, the Genesys simulator, which evaluates noise without adding any of its own. Because the insertion loss before the DUT is 0dB, T

_{1}is identical to T

_{1}

^{IN}. The final calculated noise figure from the Y-factor measurements is given by F = 10log

_{10}(1 + T

_{1}

^{IN}/290). The value obtained (4.9dB) aligns with the expected value from the parameter settings used when setting up the mixer schematic.

### Example of SSB Noise-Figure Measurement by the Y-Factor Method

**Figure 14**and the test results in

**Tables 12**and

**13**.

More detailed image (PDF, xxx)

*Figure 14. Simulation schematic to determine the SSB mixer noise figure using the Y-factor method.*

Table 12. Y-Factor Simulation Results for the DSB Mixer Measurement | |||||

B (Hz) | IL (dB)* | pinOFF (dBm) | pinON (dBm) | poutOFF (dBm) | poutON (dBm) |

100,000 | 2.2 | -123.975 | -109 | -108.015 | -101.455 |

Table 13. Y-Factor Calculations for the SSB Mixer NF Measurement | |||||||

Y_{2} |
Y_{12} |
T_{12} (K) |
T_{2} (K) |
T_{1} (K) |
T_{1}^{IN} (K) |
F (dB) | G (dB) |

31.443 | 4.529 | 2211.584 | 0 | 2211.584 | 1217.354 | 7.158 | 6.602 |

_{1}is higher than the mixer’s noise temperature T

_{1}

^{IN}, which has been calculated according to Equation 42 in the Losses Before the DUT section. The final calculated noise figure from the Y-factor measurements is given by F = 10log

_{10}(1 + T

_{1}

^{IN}/290). The value obtained is 7.158dB. This value should be compared to the value obtained with Equation 43, assuming that the image noise of the source is completely suppressed:

NF = 10log_{10} (2(10^{(4.9/10)} - 1) + 1) = 7.144dB |
(Eq. 43) |

### Example of the SSB Noise-Figure Measurement by the Padded Y-Factor Method

**Figure 15**,

**Tables 14**and

**15**).

More detailed image (PDF, xxx)

*Figure 15. Simulation schematic to determine the SSB mixer noise figure using the padded Y-factor method.*

Table 14. Y-Factor Simulation Results for the Padded SSB Mixer Measurement | |||||

B (Hz) | IL (dB)* | pinOFF (dBm) | pinON (dBm) | poutOFF (dBm) | poutON (dBm) |

100,000 | 12.2 | -123.975 | -109 | -107.272 | -106.141 |

Table 15. Y-Factor Calculations for the Padded SSB Mixer NF Measurement | |||||||

Y_{2} |
Y_{12} |
T_{12} (K) |
T_{2} (K) |
T_{1} (K) |
T_{1}^{IN} (K) |
F (dB) | G (dB) |

31.443 | 1.297 | 29392.313 | -5.98E-14 | 29392.313 | 1498.536 | 7.901 | -3.398 |

_{10}(1 + T

_{1}

^{IN}/290). The value obtained is 7.901dB. This value corresponds well to the value that would be anticipated from adding 3.0dB to the DSB noise figure of 4.9dB. Note that the use of a 10dB attenuator causes the Y-factor to get close to unity, which might endanger accuracy. When using high values of attenuation in a real-world measurement, it is advisable to select the highest ENR source available to maintain accuracy.

## Conclusion

#### References

- For more information on Agilent’s mixer thermal noise model, see http://edocs.soco.agilent.com/display/genesys2010/MIXER_BASIC.
- “IRE Standards on Electron Tubes: Definitions of Terms, 1957,”
*Proceedings of the IRE*, vol. 45, pp. 983–1010, July 1957; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4056638&isnumber=4056624. - Maas, S.,
*Microwave Mixers*, Artech House Microwave Library, Artech House, 1993. - “Telecommunications: Glossary of Telecommunication Terms,”
*Federal Standard 1037C*, June 1991; www.its.bldrdoc.gov/fs-1037/fs-1037c.htm. - “Noise Figure Measurement Accuracy—The Y-Factor Method,”
*Agilent Technologies, Application Note 57–2*, 2010; http://cp.literature.agilent.com/litweb/pdf/5952-3706E.pdf.

#### Related Parts

Low-Noise Amplifier (LNA) Solutions | |||

LNA Application | Part Number | Description/Features | Key Specifications |

GPS/GNSS | MAX2686L | LNA with integrated LDO | NF = 0.88dB, Gain = 19dB |

AM/FM Radio | MAX2180A | Variable-gain LNA for active antenna applications | Integrated power detector and antenna sense |

WLAN | MAX2692 | LNA with integrated 50Ω output matching circuit | NF = 1.1dB, Gain = 18.2dB |

RKE | MAX2634 | Optimized for 315MHz to 433.92MHz remote keyless entry | NF = 1.2dB, IIP3 = -16dBm |

HSPA/LTE | MAX2668 | Three programmable gain stages optimize linearity and sensitivity | NF = 1dB, Gain = 14.5dB |

Gain Block | MAX2612–MAX2616 | 40MHz to 4GHz broadband operation with 0.5dB gain flatness | NF = 2.1dB, OIP3 = +35.2dBm |

Mixer Solutions | |||

Mixer Type | Part Number | Description/Features | Key Specifications |

Down Conversion High Linearity | MAX19998 | High linearity mixer with integrated LO buffer and power/performance bias | RFIN = 2GHz to 4GHz, IIP3 = 24.3dBm, 2RF - 2LO = 67dBc |

Up/Down Conversion High Linearity |
MAX2042A | Ultra-wide LO frequency range supports low-side or high-side LO injection | RFIN = 1.6GHz to 3.9GHz, IIP3 = 33dBm, 2RF - 2LO = 72dBc |

Down Conversion Broadband Low Power | MAX2680/MAX2681/MAX2682 | Miniature low noise mixer, low voltage operation, and low operating current | RFIN = 400MHz to 2.5GHz, IIP3 = -1.8dBm |

Up Conversion Broadband Low Power |
MAX2660/MAX2661/MAX2663 MAX2671/MAX2673 |
Miniature low noise mixer, low voltage operation, and low operating current | RFIN = 400MHz to 2.5GHz, OIP3 = 9.6dBm |

VCO/PLL Solution | |||

VCO/PLL Type | Part Number | Description/Features | Key Specifications |

Fraction-n/Integer-n Synthesizer | MAX2870 | Ultra-wideband PLL with integrated VCO and integrated dividers | 23.5MHz to 6000MHz frequency range, -226.4dBc/Hz noise floor |