LINEAR Signal Chain Noise Analysis for RF-to-Digital Receivers Design Note 439 Cheng-Wei Pei
Contents
1. DESIGN NOTES Signal Chain Noise Analysis for RF to Digital Receivers Design Note 439 Cheng Wei Pei Introduction Designers of signal receiver systems often need to per form cascaded chain analysis of system performance from the antenna all the way to the ADC Noise is a criti cal parameter in the chain analysis because it limits the overall sensitivity of the receiver An application s noise requirement has a significant influence on the system topology since the choice of topology strives to optimize the overall signal to noise ratio dynamic range and several other parameters One problem in noise calcula tions is translating between the various units used by the components in the chain namely the RF IF baseband and digital ADC sections of the circuit Figure 1 shows a simplified system diagram There is an RF section an IF baseband section represented by an amplifier and an ADC The RF section which includes a mixer or demodulator is commonly specified using noise figure NF in a decibel scale dB This may also be specified with a noise power spectral density which is similar to NF in concept e g 160dBm Hz is RF SECTION NOISE FIGURE dB IF BASEBAND ADC nV VvHz SNR dB dn439 F01 LT5557 MIXER LTC6400 26 AMPLIFIER LTC2255 14 BIT NFpF 10 6dB Aopamp 20V V 72dB SNR Gpr 3 30B 1 4nV VHz INPUT REFERRED Vmax 0 707VRmS Figure 1 Block Diagram of2. fsamp_e Sample rate of the ADC in Hertz Inour example en apc comes outto 22 5nV Hz assum ing a 125MHz sample rate This voltage noise density enano can then be RMS summed with the amplifier Output noise density eyo and the result input referred by dividing by the gain Agpamp To convert back to NF rearrange the first equation in this article NFToTAL eN ADC eyo Aopamp n 50 0 5 20109410 Gpr dB This quantity NFToraL gives the overall input noise figure with the contributions of the RF section the amplifier and the ADC Inthe example NFtorar is 12 7dB for the entire chain of three devices Conclusion When working with an entire system design from RF components to ADC noise specifications do not always use the same units from component to component This article addresses the translation between the various nomenclatures Radio designers can use this information to design their system topology and select components for optimal sensitivity For applications help call 408 432 1900 Ext 2525 Linear Technology Corporation 1630 McCarthy Blvd Milpitas CA 95035 7417 408 432 1900 FAX 408 434 0507 www linear com dn439 LT TP 0408 392K PRINTED IN THE USA TECHNOLOGY LINEAR TECHNOLOGY CORPORATION 2008
3. the square root of the total noise bandwidth This bandwidth is limited by the amplifier circuit and any ADC antialias filtering Assuming a total bandwidth of 50MHz the integrated noise in our example is N2 375uVays The total theoretical SNR can be calculated as te where Vmax Maximum sine wave input to the ADC in Vrms Vp p 0 35 N2 total integrated noise at node 2 excluding the ADC in VRMS This theoretical SNR which is 65 5dB in the example represents the maximum resolution attainable with a perfect ADC The actual ADC should have an SNR at least 5dB above this number to maintain the performance level down the chain For example a practical high performance 14 bit ADC like Linear Technology s LTC2255 family or LTC2285 family of dual ADCs would have an SNR in the 72dB to 74dB range SNRTHEORETICAL 20 od10 Data Sheet Download www linear com SNR to NF For radio designers an important consideration in system design is total noise figure which is affected by all com ponents in the chain Once the components are selected one can determine the equivalent input noise figure and the overall sensitivity of the receiver Assuming that the signal s of interest lie within one Nyquist bandwidth of the ADC a Nyquist bandwidth is fsampLe 2 the equiv alent noise of the ADC is VMAX 1 SNR apc f A oes where SNRapc data sheet SNR at the frequency of interest in dB nV e 10 mee VHz
4. a Simplified Signal Chain with RF Components Mixer LNA etc IF Baseband Compo nents Represented by a Simple Amplifier and an ADC The Input Resistor of the Amplifier Serves as a Matched Termination for the 50Q RF Section A Suggested Product and Its Specification for Each Section Are Included equal to an NF of approximately 14dB so here we use NF When working inafixed impedance 50 environment using NF simplifies the analysis of an RF signal chain However ifthe assumptions of constant impedance and proper source load termination are not valid then NF calculations become less straightforward F baseband components suchas amplifiers are typically specified with noise spectral density which is commonly measured in volts and amps per square root Hertz nV Hz and pA VHz The contribution of current noise pA VHz is usually negligible inlowimpedance environments ADC noise is primarily specified as a signal to noise ratio SNR in decibels SNR is the ratio of the maximum input signal to the total integrated input noise of the ADC In order to perform a full signal chain analysis a designer needs to be able to translate between NF noise density and SNR NF to SNR How Much ADC Resolution The first transition is from the RF section to the IF base band section NF is a convenient unit but requires con stant system impedance Since noise spectral density is independent of impedance converting from NF to nV Hz makes se
5. nse since in the transition from RF to baseband node 1 in Figure 1 the chain is leaving the fixed 50Q environment At node 1 the noise voltage density due to the RF part of the chain can be represented as GRF NFRF idl a eosa Z where Grr cascaded gain of RF component s in dB EN RF NFpr cascaded NF of RF component s in dB en 50 noise density of 502 0 91nVams VHz at 27 C 0 5 resistive divider from load termination equal to 0 5 if Rr and Rs are 50Q 47 LT LTC and LTM are registered trademarks of Linear Technology Corporation All other trademarks are the property of their respective owners 04 08 439 With the LT5557 shown in Figure 1 engr Comes out to 2 25nV VHz The input referred voltage noise density of the IF baseband section including op amp resistors can be computed using the op amp data sheet and summed with the contribution from the RF portion using sum of squares addition since the specified values are RMS Multiplying the result by the amplifier gain V V gives the total noise density at node 2 ignoring the ADC s ef fective contribution nV en2 opamP Jenoramp 2 eure Using the LTC6400 26 amplifiers specifications eno comes out to 53nV Hz The final step is to compute the overall SNR at the ADC To do so one must know the total integrated noise at node 2 Assuming the noise spectral density is constant with frequency one can simply multiply eyo by
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LINEAR Signal Chain Noise Analysis for RF to Digital Receivers Design Note 439 Cheng Wei Pei