Budget analysis ensures good radio receiver link performance

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Budget Analysis Ensures Good Radio Receiver Link Performance
Link budget analysis in radio receiver design determines whether the system's noise and distortion performance meets the design specifications. The analysis attempts to string together the specifications of the components in the receiver chain to give you an overall view of the system's performance. The key performance factors are noise figure and IP3 (third-order intercept point). The inability to filter these factors out from the desired signal limits the receiver's sensitivity.
The signal chain reflects the single conversion architecture of a narrowband receiver for applications such as the GSM (Global System for Mobile Phones) system (Figure 1). The first low-noise amplifier, LNA1, is usually located close to the antenna to reduce cable losses and keep the noise figure as low as possible. The rest of the signal chain, starting with the second low-noise amplifier, LNA2, is placed on the receiver card inside the base station housing.
For analysis purposes, the design shows the noise figure and IP3 of each component. By performing a decibel calculation, using the gain or loss of the components in the signal chain, you can easily calculate the compound effect of the series components. If you assume a 50Ω system and no filters, the calculation is fairly simple. However, since we are now using op amps and ADCs in receiver design and do not require matching to 50Ω, we assume that a 50Ω system is invalid. Given this, you may wonder how to deal with changes in impedance. In addition, you need to understand the effect of SAW filters on interfering signals when performing an effective system link budget analysis.
Figure 1: Two SAW filters in a narrowband single conversion receiver reduce the linearity requirements of the amplifier far from the antenna.
Figure 2: Level diagrams plot the signal levels through the receiver chain
Figure 3: The logarithmic and logarithmic scales plot the input and output power of two tones on a device and their intermodulation products
Figure 4: Intermodulation products can be calculated for any input and output power when the intercept point is known
Effect of filters
The receiver signal chain includes two SAW filters. They affect interfering signals and help reduce the linearity requirements of the amplifier far from the antenna. But how do you quantify these effects and make the relevant calculations?
You can specify SAW filters by passband insertion loss at offset frequencies from the center frequency and stopband attenuation. For noise calculations, you use the passband insertion loss. For IIP3 analysis, you use the attenuation of the interfering signal. For the input, the intercept point is called IIP3; for the output, the intercept point is called OIP3 (output intercept point).
For example, the GSM specification requires an IIP3 of 0.8MHz to 1.6MHz for the signal tone, and specifies an insertion loss of 8dB at the signal frequency and 33dB attenuation above 0.6MHz for the first and second IF SAW filters. Thus, in addition to the 8dB insertion loss of each filter, you have also reduced the level of the interfering signal by 25dB, and the reduced interfering level can be used in the IIP3 analysis of the series connection to calculate the IM3 (third-order intermodulation) products.
For most of the signal chain, both the input and output need to be matched to 50Ω impedance for correct operation. In this part of the chain, voltage gain expressed in decibels is equivalent to power gain. On the other hand, op amps can have different input and output impedances. Op amps and ADCs are voltage-driven devices with high impedance inputs. Since manufacturers typically specify op amp gain in terms of voltage gain, our analysis also uses voltage gain to calculate the impedance change.
You calculate noise and intermodulation products in terms of power. To adjust the signal level to power based on the voltage gain, you should subtract the logarithm of the impedance ratio, as shown below:
Table 1: Link Budget Analysis
Link Budget Analysis LNA 1 LNA 2 Image Rejection 1st Mixer 1st IF Amplifier 1st IF SAW Filter Program Attenuation 2nd IF Amplifier 2nd IF SAW Filter 3rd IF Amplifier 4th IF Amplifier Noise Filter ADC Total
Voltage Gain (dB) 15 15 -3 -8 15 -8 -1 15 -8 20 20 -0.7 0
Voltage Gain (V/V) 31.62 31.62 0.5 0.16 31.62 0.16 0.79 31.62 0.16 100 100 0.85 1
Sum of Voltage Gains (dB) 15 30 27 19 34 26 25 40 32 52 72 71.3 71.3 71.3
Impedance Adjustment (dB) 0 0 0 0 0 0 0 0 6 0 0 6 0
Sum of Impedance Adjustment (dB) 0 0 0 0 0 0 0 0 6 6 6 12 12Filter
Interference Signal Rejection (dB) 0 0 0 0 0 25 0 0 25 0 0 0 0
Sum of Interference Rejection (dB) 0 0 0 0 0 25 25 25 25 50 50 50 50
Noise Figure AnalysisDevice
Noise Figure (dB) 2 3 3 8 3 8 4 3 8 20 28 0.7 40Device
Linear Noise Factor (Linear) 1.58 2 2 6.31 2 6.31 2.51 2 6.31 100 630.96 1.17 10,000
Sum of Linear Noise Factors (Linear) 1.58 1.62 1.62 1.63 1.64 1.64 1.65 1.65 1.65 1.9 1.91 1.91 1.93 Sum of
Noise Figures (dB) 2 2.09 2.09 2.12 2.15 2.16 2.17 2.17 2.18 2.78 2.82 2.82 2.85 2.85
Third-Order Intercept Point Analysis
Two-Tone Interferer Signal Level (dBm) -43 -28 -13 -16 -24 -9 -42 -43 -28 -67 -47 -27 -33.7 -33.7
Device Third-Order Intermodulation Intercept Point (dBm) 5 15 36 26 21 36 37 21 36 16 16 36 32
Third-order intermodulation (dBc) -96 -86 -98 -84 -90 -90 -158 -128 -128 -166 -126 -126 -131.4
Sum of third-order intermodulation intercept points (dBm) 5 -0.21 -0.33 -2.2 -2.49 -2.75 -2.75 -2.75 -2.75 -2.75 -2.75 -2.75 -2.75 -2.75
Signal level
Minimum input signal level (dBm) -104 -89 -74 -77 -85 -70 -78 -79 -64 -64 -58 -38 -44.7 -44.7
3MHz blocker level (dBm) -13 2 17 14 6 21 -12 -13 -4 -4 -17 -3 -3.7 -3.7
Third-Order Intermodulation Point (dBm) -139 -113.59 -98.34 97.61 -105.02 -89.5 -97.5 -98.5 -83.5 -83.5 -77.5 -57.5 -64.2 -64.2
Thermal Noise (dBm) -121 -104 -88.91 -91.91 -99.88 -84.85 -92.84 -93.83 -93.83 -78.83 -77.22 -52.18 -58.88 -58.88
Table 2: Definitions of Column Items in Link Budget Analysis Table
Voltage Gain (dB) Stage Voltage Gain
in decibels Voltage Gain (V/V) Linear Stage Voltage Gain
in Volts Sum of Voltage Gains (dB) Total Gain Impedance Adjustment from Input Stage to Current Stage in decibels (
dB) Ratio of output to input impedance expressed in decibels calculated using Equation 2 Sum of
impedance adjustments (dB) Total impedance adjustment from input stage to current stage expressed in decibels
Interference signal suppression by filter (dB) Interference signal attenuation expressed in decibels relative to passband insertion loss Sum of
interference signal suppression (dB) Total interference signal attenuation from input stage to current stage expressed in decibels
Device noise figure (dB) Device noise figure expressed in decibels
Device linear noise factor Device linear noise factor
Sum of linear noise factors Total linear noise factor from all stages to current stage calculated using Equation A in the Web Toolbar Sum
of noise figures (dB) Total noise figure in decibels from all stages to current stage calculated using Equation B in the Web Toolbar
Two-tone interferer level (dBm) Two-tone interferer level considering filter attenuation and impedance set to 1mW and scaled in decibels Device
third-order intermodulation intercept point (dBm) Device IIP3 expressed in decibels Specification, set to 1mW
3rd Order Intermodulation (dBc) 3rd Order Intermodulation Distortion calculated by Equation C in the Web Toolbar Sum of 3rd
Order Intermodulation Intercept Points (dBm) Total IIP3 in dB for all stages to current stage calculated by Equation 1 (set to 1mW)
Minimum Input Signal Level (dBm) In-band Signal Level in dB, set to 1mW
3MHz Blocking Level (dBm) Blocking Level Taking into account Filter Attenuation and Impedance in dB, set to 1mW
3rd Order Intermodulation Point (dBm) 3rd Order Intermodulation Product Level in dB, set to 1mW
Thermal Noise (dBm) In-band Noise Level in dB, set to 1mW
Total Total Series Link Budget for All Devices
Output Signal Level (dBm) =
Input Signal Level (dBm) + Voltage Gain - 10log10 (Output Impedance / Input Impedance)
For example, to the ADC The input impedance is 800Ω, driven by an op amp with an input impedance of 200Ω and a voltage gain of 20dB. The impedance ratio is 6dB. If the ADC full scale voltage is 2 V pp, the maximum input is -2dBm. Therefore, the maximum input to the op amp is -2 dBm - 20dB + 6dB = -16dBm. In other words, the input level to the op amp plus the 20dB gain minus the impedance ratio in dB equals the input level to the ADC.
GSM900 Requirements
GSM900 base stations require a reference sensitivity of -104dBm or better (Reference 1). Typically, the system noise must be less than 6dB, or -110dBm. The input thermal noise from the antenna is kTB, where k is the Boltzmann constant (1.38x10-23 J/K), T is the absolute temperature (3000K), and B is the bandwidth (200kHz for GSM). Therefore, kTB = -121dBm.
To meet the specification, -121dBm + NF (noise figure) must be less than -110dB. The noise figure of the radio must be less than 11dB. The benefit of using noise figure is obvious: once you know the noise figure, the sensitivity achieved due to noise reduction is very obvious.
Another major analog performance factor is linearity. The GSM900 specification requires a reference sensitivity of -104dBm in the presence of two -43dBm interferers separated by 0.8MHz and 1.6MHz from the current signal. Low-side IM3 products can obtain the required signal. Using 6 dB of headroom, the maximum value of the IM3 product is -110-(-43) = -67 dBc. Substituting this value into
IIP3 = PIN- (1)
where the IIP3 and PIN dB values are 1 mW and the IM3 dB value is determined by the carrier, the minimum value of the receiver IIP3 is:
IIP3 = -43- = -9.5 dBm
The GSM900 specification also requires that the system meet a reference sensitivity of -104 dBm in the presence of a -13 dBm interfering tone from the carrier at 3 MHz. You use this value to set the signal gain for the receiver chain in the link budget analysis.
Link Budget Analysis
Table 1 shows the link budget analysis for the receiver chain shown in Figure 1, using the following assumptions:
? The first and second IF SAW filters have 8 dB of passband insertion loss and 33 dB of stopband rejection at the interfering frequency.
? IF amplifiers 3 and 4 are op amps with 200 Ω input impedance.
? The input impedance of the ADC is 800Ω.
? The full-scale voltage at the input of the ADC is 2V pp (-2dBm).
? The analysis is performed using the GSM900 specification.
? The reference sensitivity (or minimum signal) is -104dBm.
? The blocking at 3MHz is -13dBm.
? The two-tone interferer is -43dBm.
Table 2 describes the items in the columns of Table 1. For a template for budget analysis, see the Web version of this article at www.edn.com.
You can draw a level graph to visualize the signal levels as they pass through the receive chain (Figure 2). This step can be used as a troubleshooting step to help you locate the problem area.
Figure 5: In this gain block chain for cascade IP3 analysis, each block acts as a gain GX, and the third-order intercept point at the input is the IIP3X.
The analysis shows that the receiver chain exceeds the GSM900 specification. Because of part-to-part variations, drift over temperature and time, and other factors that are difficult to quantify, it is best to leave plenty of margin in your design. You can then build the circuit and test it to see if practice matches theory. The web toolbar "Series Noise and Intermodulation Distortion Analysis" can serve as a basis for understanding.
The two interfering tones specified by GSM900 create an interfering signal to the current signal due to the effects of third-order nonlinearity. You can use IM3 to quantify the distortion caused by the nonlinearity. By comparing this value to the antenna input, you can easily determine whether the specification is met.
If the input and output power of the two tones applied to the device and their intermodulation products are plotted log-log, the fundamental tone has a slope of 1, the second-order components have a slope of 2, and the third-order components have a slope of 3 (Figure 3). The amplifier starts to compress before the curves cross. The point 1dB below the expected output power is the 1dB compression point, usually called P1. Extending each curve, you will find IP2 (second-order intercept point) and IP3.
But if you are interested in intermodulation distortion relative to the carrier and not some hypothetical point that the amplifier will never reach, then why do you need to know the intercept point and why do you care about it? The answer is that there is a mathematical relationship between intermodulation distortion and the intercept point. Knowing the intercept point, you can calculate the intermodulation products for any input/output power.
Figure 4 shows how to calculate L1 and L3 when the slope is known. Subtracting any two points on each curve, rearranging them, and subtracting them again gives:
Series Noise and Intermodulation Distortion Analysis
Figure A Series Noise Analysis Using This Gain Block Chain Series Intermodulation Distortion
Analysis Overview
Nonlinearity in the transfer function of all electronic devices produces distortion. In terms of the equation of a straight line, y=b+mx, nonlinearity refers to the deviation of the output (y) from the independent variable (x) times a constant factor (m) plus some offset constant (b).
Extending the nonlinear transfer function of a basic transistor circuit to the power supply series is a typical method for quantifying distortion components (Reference 1). For example, transistors typically have an exponential transfer function (i.e., collector current versus basic emitter voltage) y=ex, where x is the independent variable and y is the dependent variable. Extending ex to the power supply series so that x approaches zero gives:
Figure B shows the function y=ex and the estimation using increasingly more power supply series terms.
The farther x is from zero, the more terms are required to correctly estimate the value of ex. If x is less than 0.25, the linear term 1+x is an approximation of the actual function and the circuit is linear. As x increases, more and more terms are needed to correctly estimate the value of ex, and the output includes distortion terms raised to the second, third, or higher powers.
Figure B: The further x is from 0, the more terms are needed to correctly estimate the value of ex.
Table A: Distortion Component Frequencies
We can measure this with the test setup shown in Figure C. Two test tones are generated by RF1 and RF2. A directional coupler reduces the intermodulation products generated by the RF source. The output of the device under test (DUT) is measured with a spectrum analyzer. If the two tones and their second- and third-order distortion products are plotted, the result is shown in Figure D
Figure C: The directional coupler in the intermodulation test setup reduces the intermodulation products generated by the RF source.
You can use a SAW filter to reduce most of the generated distortion, but it is ineffective for third-order intermodulation products. SAW filters can also be used to reduce interfering tones outside the current band, which helps meet the IP3 requirements of the system.
Figure D: The SAW filter reduces most distortion components, but it is ineffective against third-order intermodulation products.