EE194-EE290C 28 nm SoC for IoT Acknowledgement: Wayne Stark EE455 Lecture Notes, University of Michigan
Noise Unwanted electric signals come from a variety of sources, both from - Naturally occurring noise (Atmospheric disturbances, extraterrestrial radiaoon, random electron mooon) - Human interference. (Other communicaoon systems, LighOng, ignioon etc.) One unavoidable electrical noise is the thermal mooon of electrons in conducong media - Modeled as white noise, a useful model in communicaoon. (AWGN channel) When a resistance R at a temperature T, random electron mooon produces a noise voltage v(t) a the open terminals. Consistent with the central-limit theorem, v(t) has a Gaussian distribuoon with zero mean and variance: v 2 = σ 2 v = 2 ( πkt ) 2 3h R Units: V 2
Noise v 2 = σ 2 v = 2 ( πkt ) 2 3h R Units: V 2 For all pracocal purposes, the mean square voltage spectral density of thermal noise is constant at: G v ( f ) = 2RkT Units: V 2 /Hz P a = v s ( t) / 2 2 R s = v G a ( f ) = G v( f ) 4R 2 s ( t) 4R s = kt 2 = N o 2 Units: W/Hz All frequency components in equal proporoon and is therefore called white noise. v s + - P a Z s Z L =Z * s
Noise Figure (NF) Noise figure (NF) measure the degradaoon of Signal-to-Noise raoo (SNR) caused by components in a signal chain. F = SNR in SNR out Units: Dimensionless SNR NF =10 log 10 ( F) =10 log in 10 SNR out = SNR in,db SNR out,db Units: Dimensionless It is a number by which the performance of a radio receiver can be specified. Lower the be]er.
Link Budget Friis EquaOon: P r P t = G t G r λ 4π R 2 λ P = P + G + G + 20 log r t t r 10 4π R Gain has units of db and power has units of dbm or dbw.
Example Link Budget P t (Transmit power) G t (Transmit antenna Gain) G r (Receive antenna Gain) λ (2.45 GHz) P r (Received power) Link Margin Distance (d) -5 dbm (316.2μW) 0 db 0 db 0.12491 m -75 dbm (31.6pW) 70 db ~17 m NF < R ss SNR min +174 10log 10 (BW )
Receiver NF NF < R ss SNR min +174 10 log 10 (BW ) For BLE: P e = 0.1% = 10-3 SNR = Signal Noise = E b R N o B = E b N o E b /N o depends on the type of modulaoon and demodulator.
Matlab Signal & Noise Modeling According to the sampling theorem we can represent x(t) by samples at rate 2f max. In addioon, assume that x(t) is causal so that x(t) = 0 for t < 0. The Fourier transform of x(t) is given by X( f ) = x(t) e j2π ft dt 0 = x(t)e j2π ft dt NoOce that when x(t) is real then X( f ) = X*(f ).
Matlab Signal & Noise Modeling The inverse Fourier transform is x(t) = X( f )e j2π ft df f max f max = X( f )e j2π ft df Now we can approximate these integrals with finite sums.
Matlab Signal & Noise Modeling Since the highest frequency is f max we sample at a rate 2f max. Thus the samples are separated in Ome by Δt = 1/(2f max ). Suppose we have N samples in the Ome domain. We can reconstruct these N samples in the Ome domain with just N samples in the frequency domain. The spacing in the frequency domain is Δf = 2f max /N. Since Δt = 1/(2f max ) and Δf = 2f max /N Δf Δt = 1 N That is, we are dividing the interval of the frequency response from f max to f max into N discrete frequencies and we are dividing Ome from 0 to (N 1) Δt into N discrete Ome samples.
Matlab Signal & Noise Modeling Then for f <f max X( f ) = x(t)e j2π ft dt 0 N 1 l=0 X m = X(mΔf ) = Δt x(lδt)e j2π flδt Δt N 1 x(lδt)e j2πmδflδt l=0 N 1 l=0 = Δt x(lδt)e j2πml/n
Matlab Signal & Noise Modeling Thus the above expression for X m is valid for 0 m N/2. NoOce that X m = X N m. In MATLAB the operaoon FFT takes an input vector (indexed from 1 to N) and produces an output vector (indexed from 1 to N). The input-output relaoon is X k = N n=1 j2π (k 1)(n 1)/N x n e k =1,..., N The input should correspond to the samples starong at Ome 0 up to Ome (N 1)Δt. NoOce that in order to get the correct magnitude of the frequency response we must muloply what MATLAB produces by Δt.
Matlab Signal & Noise Modeling The output samples from 1 to N/2 (when normalized appropriately) correspond to the frequency response X(0),X(Δf ),...,X((N/2)Δf) = X(f max Δ f). The samples from N/2 + 2 to N correspond to the frequency response from X( f max + Δf ),...X( Δf ). The order can be reversed into the logical order with the MATLAB command kshil.
Matlab Signal & Noise Modeling Matlab Index Frequency Matlab Index Frequency 1 0 N/2+1 -f max 2 Δf N/2+2 -f max +Δf 3 2Δf N/2+k -f max +(k-1) Δf m (m-1) Δf N/2+(fmax-f2)/Δf +1 -f 2 (f1/δf)+1 f 1 N-1-2Δf N/2 f max -Δf N -Δf
Matlab Signal & Noise Modeling N/2+1 N 1 2 N/2 -f max -f 2 - f 0 - f -f 1 f max - f
Matlab FFT Caveat
SimulaOng Noise In a computer simulaoon of a communicaoon system we represent a cononuous Ome signal with samples according to the sampling theorem. A signal can be represented if the highest frequency content is less than half the sampling rate. Thus if f s represents the sampling rate the simulaoon bandwidth is f s /2. If we consider white Gaussian noise the noise has equal power at all frequencies up to the simulaoon bandwidth.
SimulaOng Noise Thus the power spectral density of the noise in the simulaoon is S n ( f ) = N 0 / 2 f s / 2 < f < f s / 2 The noise samples (with this finite bandwidth) have variance σ 2 = f s /2 S n ( f )df = f s /2 f s /2 f s /2 N o 2 df = N o f max
Digital Baseband Block Diagram Nordic: nrf52840 Datasheet.
Power Management RF LDO 0.8V 250μA 1.5V-0.9V DC/DC Converter Digital LDO 0.8V 500μA Analog LDO 0.8V 200μA PTAT IRef 10μA±15% 1μA±15% 10nA±15% Temp. Sensor To ADC BG Vref 0.8V±20% Tunable POR BDet.
Nordic: nrf52840 Datasheet. Reset Signals
Rx Signal Flow IL: -1dB Gain:15dB NF: 1-2dB Band LNA Select Filter 2400-2483 MHz LO LPF PGA Channel Select Filter ADC F total = F 1 + F 2 1 G 1 + F 3 1 G 1 G 2 + F 4 1 G 1 G 2 G 3 +...
TRx RF LO 2f o Gaussian Pulse Shaping Tx Data from RISC V I 2 Q Matching Network PA Dummy Image Channel Clock & Rx Data Rejection Filter Data Recovery Clk Power Management Passive Mixers Timing IF Gain BPF Filter IF Gain N-bit ADC Bandgap Vref Temp. sensor Relaxation oscillator RISC V PTAT Iref Power-on-Reset (POR) clock generation LDO