diff options
Diffstat (limited to 'module-design.typ')
| -rw-r--r-- | module-design.typ | 152 |
1 files changed, 69 insertions, 83 deletions
diff --git a/module-design.typ b/module-design.typ index c9bb128..4880496 100644 --- a/module-design.typ +++ b/module-design.typ @@ -1,4 +1,4 @@ -#import "@preview/unify:0.8.1": num, qty, qtyrange, unit +#import "unify.typ": num, qty, qtyrange, unit #import "@preview/diverential:0.3.0": * = Module design <module-design> @@ -10,7 +10,7 @@ demanding requirements of the Metrologic tier. The challenge is substantial. The Metrologic tier demands $qty(10, "ppm")$ precision, $qty(90, "dB")$ signal-to-noise ratio, and -$qty(0.014, "ppm per hour", per: "/")$ drift over a DC to $qty(20, "kHz")$ bandwidth. +$qty(0.014, "ppm per hour")$ drift over a DC to $qty(20, "kHz")$ bandwidth. These specifications, taken together, require that a $qty(20, "V")$ signal range be resolved to $qty(200, "uV")$, that noise remain below $qty(632.455, "uVrms")$, and that accumulated drift not exceed $qty(10, "ppm")$ over thirty days of @@ -107,7 +107,7 @@ operators. table( columns: 4, table.header([Symbol], [Definition], [Value], [Unit]), - [$k_B$], [Boltzmann constant], [$num("1.381e-23")$], [$unit("joule per kelvin", per: "/")$], + [$k_B$], [Boltzmann constant], [$num("1.381e-23")$], [$unit("joule per kelvin")$], [$T$], [Absolute temperature], [N/A], [$unit(K)$], [$e$], [Elementary charge], [$num("1.603e-19")$], [$unit(C)$], @@ -128,7 +128,7 @@ operators. [$L$], [Inductance], [$unit(H)$], [$P$], [Power], [$unit(W)$], [$f$], [Frequency], [$unit("Hz")$], - [$omega$], [Angular frequency ($omega = 2 pi f$)], [$unit("radian per second", per: "/")$], + [$omega$], [Angular frequency ($omega = 2 pi f$)], [$unit("radian per second")$], [$tau$], [Time constant ($tau = upright("RC") "or" upright("L/R")$)], [$unit(s)$], @@ -180,18 +180,18 @@ operators. [$Z_"in"$], [Input impedance], [$unit("ohm")$], [$Z_"out"$], [Output impedance], [$unit("ohm")$], [$upright("GBW")$], [Gain-bandwidth product], [$unit("Hz")$], - [$upright("SR")$], [Slew rate], [$unit("volt per micro second", per: "/")$], + [$upright("SR")$], [Slew rate], [$unit("volt per micro second")$], [$upright("CMRR")$], [Common-mode rejection ration], [$unit("dB")$], [$upright("PSRR")$], [Power supply rejection ratio], [$unit("dB")$], - [$upright("TC")$], [Temperature coefficient], [$unit("ppm per celsius", per: "/")$], + [$upright("TC")$], [Temperature coefficient], [$unit("ppm per celsius")$], - [$V_"CR"$], [Voltage coefficient of resistance], [$unit("ppm per volt", per: "/")$], + [$V_"CR"$], [Voltage coefficient of resistance], [$unit("ppm per volt")$], - [$V_"CC"$], [Voltage coefficient of capacitance], [$unit("ppm per volt", per: "/")$], + [$V_"CC"$], [Voltage coefficient of capacitance], [$unit("ppm per volt")$], [$upright("DA")$], [Dielectric absorption], [$unit("percent")$], - [$S$], [Seebeck coefficient], [$unit("micro volt per celsius", per: "/")$], - [$theta$], [Thermal resistance], [$unit("celsius per watt", per: "/")$], + [$S$], [Seebeck coefficient], [$unit("micro volt per celsius")$], + [$theta$], [Thermal resistance], [$unit("celsius per watt")$], ), caption: [Circuit and component parameters], ) <table-circuit-and-component-parameters> @@ -214,7 +214,7 @@ operators. [$epsilon_"gain"$], [Gain error], [$unit("ppm")$], [$epsilon_"ratio"$], [Ratio error for matched components], [$unit("ppm")$], [$epsilon_"thermal"$], [Thermally-induced error], [$unit("ppm")$], - [$dv(epsilon, t)$], [Drift rate], [$unit("ppm per hour", per: "/")$], + [$dv(epsilon, t)$], [Drift rate], [$unit("ppm per hour")$], [$S_y^p$], [Sensitivity of $y$ to parameter $p$], [dimensionless], [$upright("SNR")$], [Signal-to-noise ratio], [$unit("dB")$], [$upright("RTI")$], [Referred-to-input], [$unit("uV")$], @@ -230,15 +230,15 @@ operators. table( columns: 3, table.header([Symbol], [Definition], [Typical unit]), - [$e_n$], [Voltage noise spectral density], [$unit("nano volt per shertz", per: "/")$], + [$e_n$], [Voltage noise spectral density], [$unit("nano volt per shertz")$], [$upright(i)_n$], [Current noise spectral density], - [$unit("pico ampere per shertz", per: "/")$ or $unit("femto ampere per shertz", per: "/")$], + [$unit("pico ampere per shertz")$ or $unit("femto ampere per shertz")$], - [$e_(n,"white")$], [White noise component], [$unit("nano volt per shertz", per: "/")$], + [$e_(n,"white")$], [White noise component], [$unit("nano volt per shertz")$], - [$e_(n,1/f)$], [$1/f$ noise component], [$unit("nano volt per shertz", per: "/")$ at $qty(1, "Hz")$], + [$e_(n,1/f)$], [$1/f$ noise component], [$unit("nano volt per shertz")$ at $qty(1, "Hz")$], [$f_c$], [Noise corner frequency ($1/f$ to white)], [$unit("Hz")$], @@ -276,14 +276,14 @@ operators. [$T$], [Temperature (absolute)], [$unit("K")$], [$delta upright(T)$], [Temperature difference], [$unit("celsius")$ or $unit("K")$], - [$(Delta T)/(upright(d) y)$], [Vertical temperature gradient], [$unit("celsius per centi meter", per: "/")$], + [$(Delta T)/(upright(d) y)$], [Vertical temperature gradient], [$unit("celsius per centi meter")$], - [$theta_"conv"$], [Convective thermal resistance], [$unit("celsius per watt", per: "/")$], + [$theta_"conv"$], [Convective thermal resistance], [$unit("celsius per watt")$], - [$theta_"cond"$], [Conductive thermal resistance], [$unit("celsius per watt", per: "/")$], + [$theta_"cond"$], [Conductive thermal resistance], [$unit("celsius per watt")$], [$accent(Q, dot)$], [Heat flux], [$unit("W")$], - [$accent(m, dot)$], [Mass flow rate], [$unit("kilo gram per second", per: "/")$], + [$accent(m, dot)$], [Mass flow rate], [$unit("kilo gram per second")$], [$c_p$], [Specific heat capacity], [$unit("J")/(unit("kg") dot unit("K"))$], ), @@ -387,8 +387,8 @@ Standard SI prefixes are used throughout: flicker noise). Drift errors require continuous compensation or periodic recalibration. / Drift Rate: The rate at which a parameter changes over time, typically - specified in $unit("ppm per hour", per: "/")$. The SAME Metrologic tier specifies a - maximum drift rate of $qty(0.014, "ppm per hour", per: "/")$. + specified in $unit("ppm per hour")$. The SAME Metrologic tier specifies a + maximum drift rate of $qty(0.014, "ppm per hour")$. / Precision: A measure of how closely repeated measurements or computations agree with each other, expressed as the maximum acceptable deviation from the ideal value. The SAME Metrologic tier specifies $qty(10, "ppm")$ @@ -420,7 +420,7 @@ Standard SI prefixes are used throughout: === Component terminology <component-terminology> / Temperature Coefficient (Tempco): The rate at which a component parameter - changes with temperature, typically specified in $unit("ppm per celsius", per: "/")$. + changes with temperature, typically specified in $unit("ppm per celsius")$. Lower tempco indicates greater temperature stability. / Voltage Coefficient of Resistance ($V_"CR"$): The rate at which resistance changes with applied voltage, specified in $unit("ppm per volt")$ @@ -429,7 +429,7 @@ Standard SI prefixes are used throughout: / Voltage Coefficient of Capacitance ($V_"CC"$): The rate at which capacitance changes with applied voltage. Class 2 ceramic capacitors (X7R, X5R) can exhibit $V_"CC"$ of - $qtyrange(-30, -80, "percent", delimiter: "\"to\"")$ at rated voltage, making + $qtyrange(-30, -80, "percent")$ at rated voltage, making them unsuitable for signal paths. / Dielectric Absorption ($upright("DA")$): A memory effect in capacitors where rapid charge/discharge cycles leave residual polarization that manifests as @@ -441,8 +441,8 @@ Standard SI prefixes are used throughout: exist. / Seebeck Coefficient: The voltage generated per degree of temperature difference at a thermocouple junction, specified in - $unit("micro volt per celsius", per: "/")$. Copper-to-Kovar junctions have coefficients - around $qty(40, "micro volt per celsius", per: "/")$. + $unit("micro volt per celsius")$. Copper-to-Kovar junctions have coefficients + around $qty(40, "micro volt per celsius")$. / Matched Components: Components fabricated together on a common substrate or selected to have closely tracking parameter values. Matching reduces ratio errors even when absolute tolerances are significant. @@ -452,8 +452,8 @@ Standard SI prefixes are used throughout: ($qty(100, "ppm")$) or better. / Tracking Temperature Coefficient: The difference in temperature coefficients between matched components. Well-matched components have tracking tempcos - below $qty(2, "ppm per celsius", per: "/")$ even when individual tempcos are - $qty(25, "ppm per celsius", per: "/")$. + below $qty(2, "ppm per celsius")$ even when individual tempcos are + $qty(25, "ppm per celsius")$. === Amplifier and circuit terminology <amplifier-and-circuit-terminology> @@ -475,7 +475,7 @@ Standard SI prefixes are used throughout: voltage variations. $upright("PSRR")$ degrades with frequency, making high-frequency supply noise more problematic. / Open-Loop Gain ($A_"OL"$): The gain of an amplifier without feedback, - typically $106$ to $108$ ($qtyrange(120, 160, "dB", delimiter: "\"to\"")$) for precision op-amps. + typically $106$ to $108$ ($qtyrange(120, 160, "dB")$) for precision op-amps. Finite open-loop gain creates closed-loop gain error proportional to $G_"ideal"/A_"OL"$. / Gain-Bandwidth Product ($upright("GBW")$): The product of an op-amp's DC @@ -483,7 +483,7 @@ Standard SI prefixes are used throughout: single-pole op-amp, $upright("GBW")$ is constant and determines gain error at frequency. / Slew Rate: The maximum rate of change of an op-amp's output voltage, typically - specified in $unit("volt per micro second", per: "/")$. Insufficient slew rate causes + specified in $unit("volt per micro second")$. Insufficient slew rate causes distortion for large, fast signals. / Settling Time: The time required for an amplifier output to settle within a specified error band after a step input. Settling to $qty(10, "ppm")$ @@ -491,7 +491,7 @@ Standard SI prefixes are used throughout: / Chopper Stabilization: A technique that eliminates low-frequency errors by periodically reversing signal polarity and correcting for the resulting offset. Chopper-stabilized amplifiers achieve offset drifts below - $qty(0.05, "micro volt per celsius", per: "/")$. + $qty(0.05, "micro volt per celsius")$. / Loop Gain: The product of forward gain $A$ and feedback factor $beta$ in a feedback system. Loop gain determines error suppression: errors in the forward path are divided by $(1 + A beta)$. @@ -541,7 +541,7 @@ Standard SI prefixes are used throughout: rail indicates whether a module should operate at $qty(0, "degree")$ or $qty(90, "degree")$ phase relative to the Master Oscillator. / Phase Noise: Random fluctuations in the phase of an oscillator signal, which - manifest as timing jitter. Low phase noise ($lt.eq qty(-140, "dBc per hertz", per: "/")$ + manifest as timing jitter. Low phase noise ($lt.eq qty(-140, "dBc per hertz")$ at $qty(1, "kHz")$ offset) is essential for high-precision PWAM. / Jitter: Random variations in the timing of signal transitions. Clock jitter converts directly to amplitude noise in PWAM systems. @@ -552,7 +552,7 @@ Standard SI prefixes are used throughout: matched components along lines of constant temperature to ensure identical thermal environments. / Thermal Gradient: The spatial rate of change of temperature across a surface - or volume, typically expressed in $unit("celsius per centi meter", per: "/")$. Thermal + or volume, typically expressed in $unit("celsius per centi meter")$. Thermal gradients cause matched components to experience different temperatures, degrading their matching. / Ovenization: The practice of enclosing a critical component (typically a @@ -612,7 +612,7 @@ Standard SI prefixes are used throughout: / Shielding Effectiveness: The attenuation of electromagnetic fields provided by a conductive enclosure, typically specified in $unit("dB")$. The SAME cassette provides $gt qty(20, "dB")$ shielding from - $qtyrange(80, 1000, "MHz", delimiter: "\"to\"")$. + $qtyrange(80, 1000, "MHz")$. === Module category terminology <module-category-terminology> @@ -651,7 +651,7 @@ Standard SI prefixes are used throughout: <manufacturing-and-assembly-terminology> / Burn-In: A period of powered operation (typically - $qtyrange(168, 1000, "hour", delimiter: "\"to\"")$) that accelerates initial component + $qtyrange(168, 1000, "hour")$) that accelerates initial component stabilization before final calibration. / Surface Insulation Resistance ($upright("SIR")$): The resistance between adjacent conductors on a PCB surface, affected by flux residue, contamination, @@ -700,7 +700,7 @@ Metrologic tier specifications for signals crossing that boundary. For example, a module converting SAME signals to consumer line-level audio (nominally $plus.minus qty(1, "V")$, with typical THD+N specifications of -$qtyrange(0.001, 0.01, "percent", delimiter: "\"to\"")$) cannot deliver +$qtyrange(0.001, 0.01, "percent")$) cannot deliver $qty(10, "ppm")$ precision on the audio side regardless of the quality of the conversion circuitry. The interface module documentation must clearly state the precision limitations imposed by the external format. @@ -975,7 +975,7 @@ SAME Metrologic tier specifications are achievable: table.header([Parameter], [Requirement]), [Precision], [$qty(10, "ppm")$ ($qty(0.001, "percent")$)], [Signal-to-noise ratio], [$qty(90, "dB")$], - [Drift rate], [$lt.eq qty(0.014, "ppm per hour", per: "/")$], + [Drift rate], [$lt.eq qty(0.014, "ppm per hour")$], [Bandwidth], [DC to $qty(20, "kHz")$], [Drift-free operation], [$qty(30, "day")$], ), @@ -1090,10 +1090,10 @@ continuous computation. ==== Drift rate and long-term stability <drift-rate-and-long-term-stability> -The drift rate specification of $qty(0.014, "ppm per hour", per: "/")$ means: +The drift rate specification of $qty(0.014, "ppm per hour")$ means: $ - dv(epsilon, t) lt.eq num("0.014e-6") times qty(20, "volt per hour", per: "/") = qty(280, "nano volt per hour", per: "/") + dv(epsilon, t) lt.eq num("0.014e-6") times qty(20, "volt per hour") = qty(280, "nano volt per hour") $ Over 30 days (720 hours), the accumulated drift is: @@ -1105,7 +1105,7 @@ systematic error budget. After 30 days, recalibration is required. / Important: The drift specification is a rate, not an absolute value. A module may have an initial offset of $qty(5, "ppm")$ (within spec) and drift at - $qty(0.014, "ppm per hour", per: "/")$. After 15 days, it reaches $qty(10, "ppm")$ total + $qty(0.014, "ppm per hour")$. After 15 days, it reaches $qty(10, "ppm")$ total and is now at the edge of specification. To guarantee a 30-day drift-free computation period, active compensation topologies must trim or null $epsilon_"initial"$ to near-zero ($lt qty(0.5, "ppm")$) at $t = 0$. @@ -1193,7 +1193,7 @@ absolute temperature $T$ is: $ e_n = sqrt(4 k_B T R) $ Where: -- $k_B = qty("1.381e-23", "joule per kelvin", per: "/")$ (Boltzmann constant), +- $k_B = qty("1.381e-23", "joule per kelvin")$ (Boltzmann constant), - $T =$ absolute temperature ($unit(K)$), - $R =$ resistance ($unit("ohm")$). @@ -1262,7 +1262,7 @@ Op-amp input voltage noise arises from two mechanisms: ====== Mathematical model <opamp-voltage-noise-mathematical-model> Op-amp voltage noise is specified as a spectral density -$e_n (f)$ in $unit("nano volt per shertz", per: "/")$: +$e_n (f)$ in $unit("nano volt per shertz")$: $ e_n (f) = sqrt(e_(n,"white")^2 + (e_(n,1/f)^2)/f) = e_(n,"white") sqrt(1 + f_c/f) @@ -1290,24 +1290,18 @@ servo loop. table( columns: 4, table.header([Op-amp class], [$e_(n,"white")$], [$f_c$], [Notes]), - [General purpose (TL07x)], [$18 unit("nano volt per shertz", per: "/")$], [$qty(200, "Hz")$], [JFET input], + [General purpose (TL07x)], [$18 unit("nano volt per shertz")$], [$qty(200, "Hz")$], [JFET input], - [Low noise (OPA211)], [$1.1 unit("nano volt per shertz", per: "/")$], [$qty(10, "Hz")$], [Bipolar input], + [Low noise (OPA211)], [$1.1 unit("nano volt per shertz")$], [$qty(10, "Hz")$], [Bipolar input], - [Precision low noise (LT1028)], - [$0.85 unit("nano volt per shertz", per: "/")$], - [$qty(3.5, "Hz")$], - [Bipolar input], + [Precision low noise (LT1028)], [$0.85 unit("nano volt per shertz")$], [$qty(3.5, "Hz")$], [Bipolar input], - [Chopper stabilized (LTC2057)], - [$7 unit("nano volt per shertz", per: "/")$], - [$lt qty(1, "Hz")$], - [No $1/f$ corner], + [Chopper stabilized (LTC2057)], [$7 unit("nano volt per shertz")$], [$lt qty(1, "Hz")$], [No $1/f$ corner], ), caption: [Op-amp voltage noise typical magnitudes], ) <table-opamp-voltage-noise-typical-magnitude> -For a precision op-amp ($1 unit("nano volt per shertz", per: "/"), f_c = qty(10, "Hz")$) +For a precision op-amp ($1 unit("nano volt per shertz"), f_c = qty(10, "Hz")$) over $qty(0.001, "Hz")$ to $qty(20, "kHz")$: $ @@ -1327,7 +1321,7 @@ amplifier, output noise is $10 times$ input voltage noise. ====== Compensation strategy <opamp-voltage-noise-compensation-strategy> -- Select low noise bipolar op-amps ($e_n < 2 unit("nano volt per shertz", per: "/")$) for +- Select low noise bipolar op-amps ($e_n < 2 unit("nano volt per shertz")$) for low-source-impedance nodes, - Minimize closed-loop gain stages in initial processing stages, - Use chopper-stabilized amplifiers where $1/f$ where drift dominates @@ -1346,7 +1340,7 @@ due to their extremely low bias currents. ====== Mathematical model <opamp-current-noise-mechanical-model> -Current noise spectral density $i_n$ in $unit("pico ampere per shertz", per: "/")$ flows +Current noise spectral density $i_n$ in $unit("pico ampere per shertz")$ flows through the source impedance $Z_"source"$ seen by the op-amp terminal, generating an equivalent input voltage noise: @@ -1362,16 +1356,16 @@ $ V_(n,i,"rms") = i_n times Z_"source" times sqrt(upright("BW")) $ table( columns: 3, table.header([Op-amp class], [$i_n$], [Notes]), - [Bipolar (LT1028)], [$1 unit("pico ampere per shertz", per: "/")$], [Low voltage noise, moderate current noise], + [Bipolar (LT1028)], [$1 unit("pico ampere per shertz")$], [Low voltage noise, moderate current noise], - [JFET (OPA627)], [$2.5 unit("femto ampere per shertz", per: "/")$], [Negligible], + [JFET (OPA627)], [$2.5 unit("femto ampere per shertz")$], [Negligible], - [CMOS (LMC6001)], [$0.13 unit("femto ampere per shertz", per: "/")$], [Negligible], + [CMOS (LMC6001)], [$0.13 unit("femto ampere per shertz")$], [Negligible], ), caption: [Op-amp current noise typical magnitudes], ) <table-opamp-current-noise-typical-magnitude> -For a bipolar op-amp ($1 unit("pico ampere per shertz", per: "/")$) with $qty(10, "kilo ohm")$ +For a bipolar op-amp ($1 unit("pico ampere per shertz")$) with $qty(10, "kilo ohm")$ source impedance over $qty(20, "kHz")$: $ @@ -1412,7 +1406,7 @@ and $i_(n-)$ are uncorrelated shot-noise sources. Mitigation requires: Fluctuations and high-frequency ripple on the power supply rails couple into the signal path through finite Power Supply Rejection Ratio ($upright("PSRR")$). Because $upright("PSRR")$ degrades with frequency at approximately -$qty(-20, "decibel per decade", per: "/")$, high-frequency supply ripple poses a +$qty(-20, "decibel per decade")$, high-frequency supply ripple poses a significantly greater threat to precision than DC supply variations. ====== Mathematical model <power-supply-noise-coupling-mathematical-model> @@ -1508,7 +1502,7 @@ $ V_(upright("DC"),"error") = alpha dot V_("induced") $ <radiated-and-conducted-rf-interference-typical-magnitude> For a $l = qty(1, "m")$ unshielded banana patch cable in an -$E = qty(3, "volt per meter", per: "/")$ ambient RF field (per EN-6100-4-3 +$E = qty(3, "volt per meter")$ ambient RF field (per EN-6100-4-3 specification limit) with coupling efficiency $eta = 0.1$: $ V_("induced") = 3 times 1 times 0.1 = qty(300, "mVpp") $ @@ -1545,7 +1539,7 @@ budget. Induced RF voltage scales linearly with electric field strength $E$ and cable length $l$. Attenuation from passive RC low-pass filters scales at -$qty(-20, "decibel per decade", per: "/")$ per filter pole above the cutoff +$qty(-20, "decibel per decade")$ per filter pole above the cutoff frequency. ====== Compensation strategy @@ -1602,7 +1596,7 @@ $ For external equipment connections, laboratory safety ground potential differences $Delta V_G$ typically range from -$qtyrange(1, 100, "mV", delimiter: "\"to\"")$. Without differential rejection, a +$qtyrange(1, 100, "mV")$. Without differential rejection, a $qty(10, "mV")$ ground offset introduces a catastrophic $qty(10, "mV")$ ($qty(500, "ppm")$) error. @@ -1627,7 +1621,7 @@ $ Intra-chassis ground error scales linearly with module return current $I_("return")$ and AGND copper resistance $R_(upright("AGND"))$. Inter-chassis ground error scales inversely with Interface Module -$upright("CMRR")_(unit("dB"))$ at $qty(20, "decibel per decade", per: "/")$. +$upright("CMRR")_(unit("dB"))$ at $qty(20, "decibel per decade")$. ====== Compensation strategy <ground-loop-currents-compensation-strategy> @@ -1744,7 +1738,7 @@ Triboelectric induced noise voltage in a flexible cable is modeled as: $ V_("tribo") = k_("tribo") dv(L, t) $ Where $k_("tribo")$ is the cable's triboelectric coupling constant in -$unit("mV") / unit("meter per second", per: "/")$ and $dv(L, t)$ is the rate of mechanical +$unit("mV") / unit("meter per second")$ and $dv(L, t)$ is the rate of mechanical deformation. Piezoelectric microphonic voltage generated across a capacitor of capacitance @@ -1759,22 +1753,22 @@ dielectric material. <triboelectric-and-piezoelectric-effects-typical-magnitude> For a standard PVC-insulated patch cable, -$k_("tribo") approx qty(50, "milli volt per meter per second", per: "/")$ -experiencing mild flexing ($dv(L, t) = qty(1, "milli meter per second", per: "/")$): +$k_("tribo") approx qty(50, "milli volt per meter per second")$ +experiencing mild flexing ($dv(L, t) = qty(1, "milli meter per second")$): $ V_("tribo") = num("50e-3") times num ("1e-3") = qty(50, "uV") (qty(2.5, "ppm")) $ Using a low-noise graphite-coated cable -($k_("tribo") approx qty(1, "milli volt per meter per second", per: "/")$): +($k_("tribo") approx qty(1, "milli volt per meter per second")$): $ V_("tribo") = num("1e-3") times num("1e-3") = qty(1, "uV") (qty(0.05, "ppm")) $ For an X7R ceramic capacitor -($d_33 approx qty(200, "pico coulomb per newton", per: "/")$) subjected to a +($d_33 approx qty(200, "pico coulomb per newton")$) subjected to a $qty(1, "g")$ ($qty(0.1, "N")$) acoustic/mechanical vibration spike on a $qty(100, "nF")$ node: @@ -1942,33 +1936,25 @@ materials. columns: 5, table.header([Inductor type], [$upright("DCR")$], [Core loss ($qty(10, "kHz")$)], [Self-resonance], [Notes]), [Air core], - [High ($qtyrange(1, 100, "ohm", delimiter: "\"to\"")$)], + [High ($qtyrange(1, 100, "ohm")$)], [None], [High ($gt qty(100, "MHz")$)], [No saturation, no core noise], [Ferrite bead], - [$qtyrange(0.1, 1, "ohm", delimiter: "\"to\"")$], + [$qtyrange(0.1, 1, "ohm")$], [Very high], - [$qtyrange(10, 100, "MHz", delimiter: "\"to\"")$], + [$qtyrange(10, 100, "MHz")$], [Designed for loss (filtering)], - [Ferrite inductor], - [$qtyrange(0.1, 10, "ohm", delimiter: "\"to\"")$], - [Moderate], - [$qtyrange(1, 50, "MHz", delimiter: "\"to\"")$], - [General purpose], + [Ferrite inductor], [$qtyrange(0.1, 10, "ohm")$], [Moderate], [$qtyrange(1, 50, "MHz")$], [General purpose], - [Powdered iron], - [$qtyrange(0.5, 5, "ohm", delimiter: "\"to\"")$], - [Low], - [$qtyrange(1, 10, "MHz", delimiter: "\"to\"")$], - [DC bias tolerant], + [Powdered iron], [$qtyrange(0.5, 5, "ohm")$], [Low], [$qtyrange(1, 10, "MHz")$], [DC bias tolerant], [Laminated steel], - [$qtyrange(0.1, 1, "ohm", delimiter: "\"to\"")$], + [$qtyrange(0.1, 1, "ohm")$], [Low at audio rate], - [$qtyrange(0.01, 1, "MHz", delimiter: "\"to\"")$], + [$qtyrange(0.01, 1, "MHz")$], [Audio transformers], ), caption: [Inductor losses and parasitic effects typical magnitudes], |