A 0.18 μm CMOS low noise, highly linear continuous-time seventh-order elliptic low-pass filter

A 0.18 µm CMOS Low Noise, Highly Linear Continuous-Time Seventh-Order Elliptic Low-Pass Filter Juan F. Fernández-Bootello*, Manuel Delgado-Restituto and Angel Rodríguez-Vázquez Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC) Edificio CICA-CNM, Avda Reina Mercedes s/n, 41012-Sevilla, SPAIN emails: {bootello|mandel|[email protected]} ABSTRACT This paper presents a fast procedure for the system-level evaluation of noise and distortion in continuous-time integrated filters. The presented approach is based on Volterra’s series theory and matrix algebra manipulation. This procedure has been integrated in a constrained optimization routine to improve the dynamic range of the filter while keeping the area and power consumption at a minimum. The proposed approach is demonstrated with the design, from system- to physical-level, of a seventh-order low-pass continuous-time elliptic filter for a high-performance broadband power-line communication receiver. The filter shows a nominal cut-off frequency of , less than ripple in the pass-band, and a maximum stop-band rejection of . Additionally, the filter features programmable boost in the pass-band to counteract high frequency components attenuation. Taking into account its wideband transfer characteristic, the filter has been implemented using Gm-C techniques. The basic building block of its structure, the transconductor, uses a source degeneration topology with local feedback for linearity improving and shows a worst-case intermodulation distortion of -70 dB for two tones close to the passband edge, separated by , with of amplitude. The filter combines very low noise (peak root spectral noise density below ) and high linearity (more than of MTPR for a DMT signal of amplitude) properties. The filter has been designed in a 0.18µm CMOS technology and it is compliant with industrial operation conditions (-40 to 85ºC temperature variation and ±5% power supply deviation). The filter occupies 13mm2 and exhibits a typical power consumption of 450 mW from a 1.8V voltage supply. Keywords: Low-noise, Continuous-Time Filters, Gm-C Filters, CAD tools for VLSI 1. INTRODUCTION Filters are essential blocks in communications systems to reject undesired signals which may be orders of magnitude larger than the desired one. Hence, the design of these filters need a special attention in the design of such communication systems. There are many factors which degrade the behaviour of monolithic filters. One key figure of merit which measures such degradation is the dynamic range (DR) of the circuit, which can be defined as the ratio among the maximum signal power level (for a given distortion at the output) which can be processed by the filter and the in-band integrated noise power1,2. It can be demonstrated that the DR is directly related with the power consumption of the filter3. Thus, from a design perspective, the availability of fast procedures for the early system-level evaluation of noise and distortion in filters which takes into account imperfections of circuit elements is essential. In this paper, we present a simple procedure for the evaluation of noise and distortion of continuous-time Gm-C filters, with no need of lengthy transient analysis. In particular, distortion is measured using Volterra’s series theory4, and the evaluation of dynamic range can be done by simple matrix algebra, amenable for computer programming. Taking advantage of this fact, a constrained optimization routine has been implemented in MATLAB® which maximizes the dynamic range of a given topology while reducing the area and power consumptions of the filter5. As a demonstration of the proposed approach, the design, from system- to physical-level, of a seventh-order low-pass continuous-time elliptic filter for a high-performance broadband power-line communication receiver is also described. f c34MHz=1dB 65dB 12dB 1MHz 70mV 56nV/ Hz 64dB 0.5Vpp VLSI Circuits and Systems II, edited by José Fco. López, Francisco V. Fernández, José María López-Villegas, José M. de la Rosa, Proceedings of SPIE Vol. 5837 (SPIE, Bellingham, WA, 2005) 0277-786X/05/$15 · doi: 10.1117/12.608294 148 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use Main specifications of the filter are of cut-off frequency, more than of stopband rejection (corner at ), less than ripple in the passband, and programmable boosting from 0 to at steps. Together, severe specifications on noise and distortion performance are also demanded. Namely, the filter must exhibit less than of peak root spectral density in the passband, and more than 60dB of MTPR for different patterns of DMT signals of amplitude. The paper is structured as follows. In Sec. 2, a general representation of Gm-C filters using matrices, which is at the basis of the aforementioned approach, is first described. Then, the procedures to compute the harmonic and/or inter-mod- ulation distortion of weakly non-linear systems, as well as their noise contributions are detailed. Next, Sec. 3 describes the approach for the optimization of the dynamic range of Gm-C filters. Sec. 4 shows the system-level design of the filter used as demonstration vehicle of the proposed procedure. Sec. 5 focuses on the transconductor block, as the main building element of the architecture, and Sec. 6 shows the circuitry used for tuning. Finally, Sec. 7 presents simulations of the filter and transconductor block, and Sec. 8 gives some concluding remarks. 2. Gm-C FILTER REPRESENTATION AND EVALUATION TECHNIQUES As noted above, in order to estimate the dynamic range of a filter, both distortion and noise must be properly evaluated. In this section, the mathematical rudiments for a fast estimation of such performances are presented. In general, any linear continuous-time filter can be formulated by the following extended state-space representation, (1) where A, B, C and E are matrices, D is a scalar, is the input signal is the output signal and is the vector which represents the internal nodes. Expressing (1) in the frequency domain, the transfer function of the filter takes the form, (2) In the case of Gm-C filter structures based on simple integrators (as those in Fig.1), matrix E in (1) represents capacitances, and matrix A and B transconductances. These matrices can be built-up from LC ladder equivalent filters as shown in 5,6. Now assume that the filter is composed by weakly non-linear fully-differential transconductors. In this case the transfer characteristic of the transconductor (neglecting second-order terms) can be described as (3) where is a third-order non linearity coefficient. Using (3), equation (1) becomes (4) 34 MHz 40dB 46 MHz 1dB 12dB 2dB 60nV/ Hz 0.5Vpp Edx dt ------Ax BEi += EoCx DEi += EiEoxx1…xn [] † = Hs() Eos() Eis() ------------- CEsA–() 1– BD+== vivo vj+ vj- 2C C 2Cj 2Cj Figure 1. First order section using conventional transconductors. + − Gmi + − + −vivo vj+ vj- C 2Cj 2Cj + − Gmi + − + − 2C iG mov1a3v2 +()= a3 Edx dt ------Ax a3Ax3BEiBEi 3 +++= EoCx DEi += Proc. of SPIE Vol. 5837 149 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use From this expression, and using Volterra’s series theory, the response of the intermediate nodes to an input can be expressed as 4 (5) where (6) is the i-th order Volterra operator and is the i-th Volterra Kernel. The Laplace transformation of such multidimensional kernel is defined by (7) where is the Laplace variable in the i-th dimension. Thus for example describes the third-order behaviour of the system. These transformed Kernels can be evaluated using the following expressions (8) (9) Thus the distortion or inter-modulation of the filter can be computed at the system level, with no need of transient analysis, using (10) where is the amplitude of the tones at the input of the system. Note from (9) that the distortion depends on the magnitude of the internal nodes of the filter and, hence, it can be reduced by decreasing the voltage level of such nodes. On the other hand, the noise contribution of a transconductor with transconductance can be modelled by an output referred current source with power spectral density , where is the noise excess factor of the transconductor3. From this, the noise spectral density of a filter can be expressed as3 (11) where is the transfer function from the output of transconductor to the output of the filter, and i and l denote the output and input nodes of the transconductor, respectively. By grouping the transfer functions in a vector G, (12) it can be easily found that, (13) Thus, the output referred mean-squared noise of the filter can be evaluated as Eit() xt() H1Eit()()H3Eit)()()+= HiEit)()()…hiτ1…τi ()Eitτ1 –()…Eitτi –()τ 1…dτi d ∞– ∞ ∫ ∞– ∞ ∫ = hi.() His1…sn ,()…hiτ1…τi ()es1τ1…snτn +()–τ1…dτn d ∞– ∞ ∫ ∞– ∞ ∫ = siH3s1s2s3 ,,() H1s1 () Ei ---------------EsA–() 1– B= H3s1s2s3 ,,() Ei 3 ------------------------------ Es1s2s3 ++()A–() 1– a3AH1s1 ()H1s2 ()H1s3 ()B3 +()= HD3ω() 1 4 ---CH3jωjωjω,,() CH1jω() -----------------------------------------ρ2 = IM32ω1ω2 ±() 3 4 ---CH3jω1jω1j±ω 2 ,,() CH1jω1 () --------------------------------------------------- ρ2 = ρ Gm Sin 4kTξGm =ξ SGf() 4kTξGmli gi 2 l ∑ i ∑ = giGmli gi Gg1g2…gn † = GCsEA–() 1– = 150 Proc. of SPIE Vol. 5837 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use (14) where represents the noise contribution from the i-th internal node to the output. Note that depends inversely on the total transconductance connected at the corresponding node and, hence, it can be reduced increasing the total transconductance and, hence, the capacitance connected at this node. 3. Gm-C FILTER OPTIMIZATION Filter optimization can be seen as a constrained minimization problem in which the current consumption of the structure must be reduced as much as possible while satisfying both the objective transfer characteristic of the filter and its prescribed dynamic range, which can be estimated from (10) and (14). This implies to modifying the system representation in (1) by an optimum scaling of the filter. By means of scaling, the original matrix representation of the filter is transformed according to the algebraic mappings (15) where is a similarity matrix which scales the magnitude level of the internal nodes of the filter, and is a matrix which modifies the noise contribution from each internal node of the circuit to the output. An optimizer based on the simulatedannealing algorithm has been used to identify the optima and matrices. As initial guess for the matrix in the simulated annealing algorithm, the or scaling norm can be used1. Similarly, the initial point for the matrix can be that which obtains the same noise contributions from the internal nodes to the filter output per unit bias current7. Both the filter performance evaluation routines and the optimization engine have been integrated in the MATLAB/ SIMULINK® platform. This brings numerous advantages in terms of signal processing, high flexibility for tool expansion and simulation with other electronic subsystems. 4. FILTER DESIGN Using the approach and tools described above, a seventh order elliptic low pass Gm-C filter has been designed. Owing to the superior performance of doubly terminated LC ladder filter structures with regard to its low sensitivity to components variation, their emulation by active circuits very often constitute the candidates of choice for silicon realization3, so this emulation has been chosen to design the filter. In the optimization process the transconductor has been assumed to have a third-order non-linearity coefficient of , a noise excess factor of and a power efficiency at a voltage supply of . The optimization problem has consisted on minimizing the cost function. (16) where is the third-order intermodulation of the filter and is the total output-referred noise power, under the constrain of keeping the power consumption below 350mW. Fig.2 shows the comparison of the intermodulation ( ), the third order distortion ( ) and the spectral noise density of filter before and after the optimization process. It also illustrates that the method based on transient analysis (circles) match up with the Volterra’s one. For the distortion estimation it has been considered that the tones have an amplitude of and are separated 1 MHz. NTotal SGf()fd 0 ∞ ∫Noi i ∑ == Noi Noi ANTAT 1– ()→ BNTB→ CCT 1– → E N TET 1– ()→ T N TN T L∞L2N a30.006V 2– =ξ10= GmI⁄0.3V 1– = 1.8 V Cost IM3NTotal ×= IM3NTotal IM32ω2ω1 –() HD3 A140mV pp = Proc. of SPIE Vol. 5837 151 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use Table 1 summarizes the results obtained before and after the optimization process. It shows that for the same power consumption, the total noise and capacitance have been reduced a 9% and 18% respectively. Fig.3 shows the simplified schematic of the filter, where transconductors provide the required boosting to correct the high frequencies attenuation of the transmission channel. Table 2 and Table 3 show the number of unitary transconductors and the value of capacitors of the optimized filter. Figure 2. Intermodulation, third order distortion and noise of the non optimized filter for: (a-c) non optimized filter and (d-f) optimized filter 020 40 60 80 100 0 1 2 3 4 5x 10-8 Frequency(MHz) Noise nV/sqrt(Hz) 020 40 60 80 100 0 1 2 3 4 5x 10-8 Frequency(MHz) Noise nV/sqrt(Hz) 010 20 30 40 50 -110 -100 -90 -80 -70 -60 Frequency(MHz) IM 3 (2w2-w1) (dB) 010 20 30 40 50 -120 -115 -110 -105 -100 -95 -90 Frequency(MHz) HD 3 (dB) 010 20 30 40 50 -110 -100 -90 -80 -70 -60 Frequency(MHz) IM 3 (2w2-w1) (dB) 010 20 30 40 50 -120 -115 -110 -105 -100 -95 -90 Frequency(MHz) HD 3 (dB) (a) (b) (c) (d) (e) (f) Table 1: characteristics of the system level filter before and after the optimization Total capacitance (pF) Noise Non optimized -68 dB -99 dB 270 160 Optimized -66 dB -102dB 195 147 IM3HD3µVrms GB 152 Proc. of SPIE Vol. 5837 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 5. TRANSCONDUCTOR Fig.4(a) shows the schematic of the transconductor employed in the filter. Transistors M1, M3 and M2, M4 (enhanced by the feedback action of M5, M7 and M6, M8, respectively) ideally transfer with unity gain the input voltage of the transconductor to the pair of nominally identical degeneration resistors R1 and R2. The generated incremental current, which is ideally proportional to the input voltage as long as resistors R1 and R2 are perfectly linear, flows through the loop formed by transistors M5-M8 and it is replicated at the output by M9-M12. It can be found that the transconductance amounts (17) Table 2: Number of unitary elements per transconductor. 16 16 16 16 10 16 24 12 918189 6124 Table 3: Filter capacitances. 34.9 pF 26.1pF 59.7pF 44.2pF 29.6pF 29.6pF 31.2pF 3.68pF 14.02pF 13.85pF Figure 3. Simplified schematic of the filter. Programmable feedforward transconductors at the insets provide transfer boosting at high frequencies. GB G11 Gin C11 G12 G21 C22 G23 G32 G34 G43 C33 C44 G45 G54 C55 G56 G65 G67 G76 C66 C77 Go C13 C13 C35 C35 C57 C57 V1+ V1- V3+ V3- GB GB V1+ V1- Vin+ Vin- Vin+ Vin- Vin+ Vin- V3- V3+ Vo+ Vo- Gin G11 G12 G21 G32 G23 G43 G34 G54 G45 G65 G56 G76 G67 G77 C11 C22 C33 C44 C55 C66 C77 C13 C35 C57 Mc1 Mc1 Mc3 Mc3 Mc1 Mc2 Mc2 outp outn Mc1 Ccomp Ccomp vbiasn vref vcmf Rd1 MR1 vfc Rd2 MR2 vfc vcasp vcasn M4M6 M2 Mp R2 M8 M1 M5 M3 M10 M12 M16 M14 M9 M11 M15 M13 Cc M7 vcmf inn inp outnoutp vbiasp vQ vcasn R1 vQ vcmf aa b b Figure 4. (a) Schematic of the transconductor; (b) tunable resistor; and (c) common-mode feedback circuit. (a) (b) (c) Gm gm9 gm5 -------- Agm1 1Agm1R+ --------------------------gm9 gm5 -------- 1 R --- ⋅≈= Proc. of SPIE Vol. 5837 153 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use where is the transconductance of transistor Mj, is the resistance of R1 and R2, and is the gain of the amplifier composed by M1 and M3 (18) and is the output conductance of transistor Mj. Approximation in (17) applies for large enough values and reveals that the transconductance is inversely proportional to the degeneration resistance and can be scaled by the aspect ratio of transistors M9-M5 (or M10-M4). On the other hand, the non-linearity of the transconductor can be modelled, assuming perfect matching among equivalent elements, by a third order non-linearity coefficient given by (19) where is the current provided by the tail transistor Mp. According to (19), in order to reduce for a given transconductance, and/or must be increased. Whatever design strategy is used for improving linearity care must be taken to not severely degrade the current efficiency of the transconductor or its high-frequency performance (parasitics at nodes must be kept low). Taking into account those parasitics (18) is transformed as follows (20) where and are the capacitance and the pole associated to the nodes and is the low frequency gain of the amplifier. On the other hand, considering the frequency characteristics of such amplifier, the third order non-linearity coefficient becomes (21) Resistors R1 and R2 are implemented as shown in Fig.4(b), where transistors MR1 and MR2 are operated in the ohmic region by means of the analogue control signal . This allows to continuously vary the resistance (and thereafter, the transconductance ), what is exploited to correct variations in the cut-off frequency of the filter, as explained later on. In the structure of the Fig.4 (a), the noise excess factor is given by, (22) and, hence, it can be reduced, for a given value, by lowering the transconductances of M5, M9 and M13. This can be done by increasing their overhead voltages, taking into account the limited power supply (1.8V) and speed requirements. A small-signal analysis of Fig.4 (a) reveals that the structure presents poles and zeros approximately given by (23) where are the capacitances associated to corresponding nodes in Fig.4 (a), and is a compensation capacitor which aims to counteract the phase lag produced by the poles. Note from (22) and (23), that by decreasing the noise excess factor is reduced but the frequency response of the transconductor worsens. Thus, there is a trade-off between speed and noise. Phase response of the transconductor can be modified (Q-tuned) by controlling the current through transistors M1, M3 (and M2, M4), using terminal . Fig.4 (c) shows the common-mode feedback circuit of the transconductor. Indeed, this circuit is shared by all the paralleled transconductors connected to the same nodes of the filter in Fig.3. To avoid stability problems, two compensation capacitors connect the output nodes of the transconductors to the control node, . These capacitors must be subtracted from the integrating node. gmj RA Agm1 gds1gds3 + ------------------------- = gdsj A a3 1 8 ---1 Agm1R3I2 -----------------------   = IIM3 IA a Agm1 gds1gds3sCa ++ -----------------------------------------Ao sωa ⁄1+ ----------------------== CaωaaAo a3 1 8 ---1 Aogm1R3I2 --------------------------   1s1s2s3 ++ ωa --------------------------+   = vfc R Gmξ ξ2 3 ---g m9gm5gm13 gm9 gm5 --------++   Rgm9 gm5 --------+= Gm ωp1 gm7 Cb -------- ≈ω p2 gm11 Cd ---------- ≈ω p3 gm1 Ca -------- gm5 G -------- ≈ω z G Cc ------ ≈ Ca, Cb, CdCc gm5 vQ vcmf 154 Proc. of SPIE Vol. 5837 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use 6. TUNING CIRCUIT Fig.5 shows the circuitry used to tune the cut-off frequency and quality factor of the (slave) filter of Fig.3. It is based on a voltage-controlled biquad (master) externally driven by a precise clock reference. Transconductors in the master and slave filter are matched and controlled by the same tuning variables obtained from the circuit of Fig.5. At the angular frequency , the band-pass output voltage of the biquad (labelled obp in Fig.5) is in phase with the input and have the same amplitudes. At the same frequency, the low-pass output voltage of the biquad (labelled olp in Fig.5) also shows the same amplitude than the external reference, but they are in quadrature. By comparing the phase of olp with that of the external clock, and integrating the error signal in a capacitor, the feedback loop determines a control voltage such that the transconductance becomes , where is the frequency of the external reference. Because integrating capacitors in the biquad and the slave filter are also matched, the feedback loop allows to define the cut-off frequency of the filter in terms of . Similarly, by comparing the amplitude of obp and the external reference and integrating the errors in a capacitor, the feedback loop determines a control voltage that tunes the quality factor of the slave filter. The biquad has a quality factor , which is close to the worst case of the poles of the filter. 7. SIMULATIONS RESULTS Fig.6 (a) shows the AC characteristics of the filter in the main corners of the technological process. Fig.6 (b) shows its programmability (changing the cut-off frequency and providing boost) and Fig.6 (c) shows its spectral density of noise. To simulate the distortion of the filter, it has been excited with two tones of 140 mVpp of amplitude separated 1 MHz. Fig.7 shows its HD3 and IM3 when the frequency is swept in the range of interest. Also shows that the simulated results fit with the theoretic ones predicted by Volterra’s series theory using the third order non linearity coefficient described in (21) and using the model in (14) and (15). Fig.8 (a) shows the intermodulation of the transconductor in the same conditions like Gmu Gmu nGmu nGmu C C Olp+ Olp- Obp+ Obp- Vin+ Vinxnor Rect Rect To VQ To Vfc Q control circuit Frequency Control circuit Figure 5. Tuning circuit. ωcnGmu C⁄= vfc Gmu 2πn⁄()fclkC= f clk f clk vQ Qn8== Q 012345678910 x 10 7 –2 –1 0 1 2 Frequency (Hz) Magnitude (dB) 012345678910 x 10 7 –80 –60 –40 –20 0 Frequency (Hz) Magnitude (dB) Figure 6. a) AC characterictics of the filter. b) Programabillity of the filter. and c) Power spectral density of noise. 0 1 2 3 4 5 6 7 8 9 10 x 10 7 0 1 2 3 4 5 6 7x 10 – 8 Frequency (Hz) Noise (nV/sqrt(Hz)) 012345678910 x 10 7 –100 –80 –60 –40 –20 0 20 Frequency (Hz) Magnitude (dB) 25 MHz 40 MHz (a) (b) (c) Proc. of SPIE Vol. 5837 155 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use the filter. It shows that the linearity decreases when the frequency increases like predicts (21). Fig.8 (b) shows the response of the filter to a digital multi-tone (DMT) input of 500 mVpp of amplitude and bandwidth from 2 to 34 MHz. As can be seen, the multi-tone power ratio (MTPR) is 64 dB. In order to compare the filter with others in the literature, the third order distortion (HD3) has been simulated with an input frequency of 5 MHz to have the same conditions of simulations that theirs, i.e with an input frequency approximately a sixth of the cut-off frequency. In this conditions the filter achieves a HD3 of -49 dB @ 1.2 Vpp differential input thus showing a DR of 69 dB. Table 4 shows the main characteristics of the compared filters where FOM denotes the power per pole per edge frequency 3. Fig. 8 (c) shows the FOM vs DR of those filters where the filter proposed is in the best adjustment line. 8. CONCLUSIONS Design considerations and simulated results of a seventh order elliptic, low-pass Gm-C filter have been presented. The filter has low noise (less than power spectral density of noise) and high linearity (-49 dB for a 1.2 Vpp @ 5 MHz input). It consumes 450 mW and occupies 13 mm2 in a 0.18 CMOS technology @ 1.8 V. Also, techniques to evaluate and minimize the noise and distortion at the system level have been presented. This techniques allow to maximize the DR and are based on simple matrix manipulation and Volterra’s series theory. ACKNOWLEDGMENT This work has been partially funded by the spanish MCyT under Project TIC2003-02355 (RAICONIF). 0 5 10 15 20 25 30 35 40 45 50 -105 -100 -95 -90 -85 -80 -75 -70 -65 Frequency (MHz) Hd3 (dB) 0 5 10 15 20 25 30 35 40 45 50 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 Frequency (MHz) IM3(2w2-w1) (dB) Figure 7. (a) HD3 and (b) IM3 of the filter and its aproximation using Volterra’s series method. Figure 8. a) Intermodulation of the transconductor vs frequency. b) Response of the filter to a DMT signal. and c) Comparison of several filter design. (a) (b) (c) 00.5 11.5 22.5 33.5 4 x 10 7 –120 –100 –80 –60 –40 –20 0 Frequency (Hz) Magnitude (dB) MTPR=64.0 dB Response to a DMT signal 0 5 10 15 20 25 30 35 70 72 74 76 78 80 82 84 86 88 frequency (MHz) Magnitude (dB) Intermodulation of the transconductor vs frequency 50 55 60 65 70 75 80 10 –11 10 –10 10 –9 10 –8 Dynamic Range (dB) FOM=Power per pole/edge frequenvy (J) This work 56nV/ Hz 156 Proc. of SPIE Vol. 5837 Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 22 Jan 2020 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use