diff options
Diffstat (limited to 'module-design.typ')
| -rw-r--r-- | module-design.typ | 73 |
1 files changed, 38 insertions, 35 deletions
diff --git a/module-design.typ b/module-design.typ index 3fb5715..db968a1 100644 --- a/module-design.typ +++ b/module-design.typ @@ -1,4 +1,4 @@ -#import "@preview/unify:0.8.1": num, numrange, qty, qtyrange, unit +#import "@preview/unify:0.8.1": 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 -$qty(0.014, "ppm per hour")$ drift over a DC to $qty(20, "kHz")$ bandwidth. +$qty(0.014, "ppm per hour", per: "/")$ 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], [$num("1.381e-23")$], [$unit("joule per kelvin")$], + [$k_B$], [Boltzmann constant], [$num("1.381e-23")$], [$unit("joule per kelvin", per: "/")$], [$T$], [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 ($omega = 2 pi f$)], [$unit("radian per second")$], + [$omega$], [Angular frequency ($omega = 2 pi f$)], [$unit("radian per second", per: "/")$], [$tau$], [Time constant ($tau = upright("RC") "or" upright("L/R")$)], [$unit(s)$], @@ -180,15 +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], [$unit("volt per micro second")$], + [$upright("SR")$], [Slew rate], [$unit("volt per micro second", per: "/")$], [$upright("CMRR")$], [Common-mode rejection ration], [$unit("dB")$], [$upright("PSRR")$], [Power supply rejection ratio], [$unit("dB")$], - [$upright("TC")$], [Temperature coefficient], [$unit("ppm per celsius")$], - [$V_"CR"$], [Voltage coefficient of resistance], [$unit("ppm per volt")$], - [$V_"CC"$], [Voltage coefficient of capacitance], [$unit("ppm per volt")$], + [$upright("TC")$], [Temperature coefficient], [$unit("ppm per celsius", per: "/")$], + + [$V_"CR"$], [Voltage coefficient of resistance], [$unit("ppm per volt", per: "/")$], + + [$V_"CC"$], [Voltage coefficient of capacitance], [$unit("ppm per volt", per: "/")$], + [$upright("DA")$], [Dielectric absorption], [$unit("percent")$], - [$S$], [Seebeck coefficient], [$unit("micro volt per celsius")$], - [$theta$], [Thermal resistance], [$unit("celsius per watt")$], + [$S$], [Seebeck coefficient], [$unit("micro volt per celsius", per: "/")$], + [$theta$], [Thermal resistance], [$unit("celsius per watt", per: "/")$], ), caption: [Circuit and component parameters], ) <table-circuit-and-component-parameters> @@ -211,7 +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], [$unit("ppm per hour")$], + [$dv(epsilon, t)$], [Drift rate], [$unit("ppm per hour", per: "/")$], [$S_y^p$], [Sensitivity of $y$ to parameter $p$], [dimensionless], [$upright("SNR")$], [Signal-to-noise ratio], [$unit("dB")$], [$upright("RTI")$], [Referred-to-input], [$unit("uV")$], @@ -273,14 +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], [$unit("celsius per centi meter")$], + [$(Delta T)/(upright(d) y)$], [Vertical temperature gradient], [$unit("celsius per centi meter", per: "/")$], - [$theta_"conv"$], [Convective thermal resistance], [$unit("celsius per watt")$], + [$theta_"conv"$], [Convective thermal resistance], [$unit("celsius per watt", per: "/")$], - [$theta_"cond"$], [Conductive thermal resistance], [$unit("celsius per watt")$], + [$theta_"cond"$], [Conductive thermal resistance], [$unit("celsius per watt", per: "/")$], [$accent(Q, dot)$], [Heat flux], [$unit("W")$], - [$accent(m, dot)$], [Mass flow rate], [$unit("kilo gram per second")$], + [$accent(m, dot)$], [Mass flow rate], [$unit("kilo gram per second", per: "/")$], [$c_p$], [Specific heat capacity], [$unit("J")/(unit("kg") unit("K"))$], ), @@ -384,8 +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 $unit("ppm per hour")$. The SAME Metrologic tier specifies a - maximum drift rate of $qty(0.014, "ppm per hour")$. + specified in $unit("ppm per hour", per: "/")$. The SAME Metrologic tier specifies a + maximum drift rate of $qty(0.014, "ppm per hour", per: "/")$. / 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 $qty(10, "ppm")$ @@ -417,10 +420,10 @@ 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 $unit("ppm per celsius")$. + changes with temperature, typically specified in $unit("ppm per celsius", per: "/")$. Lower tempco indicates greater temperature stability. / Voltage Coefficient of Resistance ($V_"CR"$): The rate at which - resistance changes with applied voltage, specified in $unit("ppm")/unit("V")$ + resistance changes with applied voltage, specified in $unit("ppm per volt")$ or $unit("ppm")/unit("V")_2$. $V_"CR"$ creates nonlinearity in circuits with signal-dependent voltage across resistors. / Voltage Coefficient of Capacitance ($V_"CC"$): The rate at which @@ -438,8 +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 - $unit("micro volt per celsius")$. Copper-to-Kovar junctions have coefficients - around $qty(40, "micro volt per celsius")$. + $unit("micro volt per celsius", per: "/")$. Copper-to-Kovar junctions have coefficients + around $qty(40, "micro volt per celsius", per: "/")$. / 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. @@ -449,8 +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 $qty(2, "ppm per celsius")$ even when individual tempcos are - $qty(25, "ppm per celsius")$. + below $qty(2, "ppm per celsius", per: "/")$ even when individual tempcos are + $qty(25, "ppm per celsius", per: "/")$. === Amplifier and circuit terminology <amplifier-and-circuit-terminology> @@ -472,7 +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 $108$ ($qtyrange(120, 160, "dB")$) for precision op-amps. + typically $106$ to $108$ ($qtyrange(120, 160, "dB", delimiter: "\"to\"")$) 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 @@ -480,7 +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 $unit("volt per micro second")$. Insufficient slew rate causes + specified in $unit("volt per micro second", per: "/")$. 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 $qty(10, "ppm")$ @@ -488,7 +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 - $qty(0.05, "micro volt per celsius")$. + $qty(0.05, "micro volt per celsius", per: "/")$. / 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 $(1 + A beta)$. @@ -538,7 +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 ($lt.eq qty(-140, "dBc per hertz")$ + manifest as timing jitter. Low phase noise ($lt.eq qty(-140, "dBc per hertz", per: "/")$ 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. @@ -549,7 +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 $unit("celsius per centi meter")$. Thermal + or volume, typically expressed in $unit("celsius per centi meter", per: "/")$. Thermal gradients cause matched components to experience different temperatures, degrading their matching. / Ovenization: The practice of enclosing a critical component (typically a @@ -648,7 +651,7 @@ Standard SI prefixes are used throughout: <manufacturing-and-assembly-terminology> / Burn-In: A period of powered operation (typically - $qtyrange(168, 1000, "hour")$) that accelerates initial component + $qtyrange(168, 1000, "hour", delimiter: "\"to\"")$) 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, @@ -972,7 +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], [$lt.eq qty(0.014, "ppm per hour")$], + [Drift rate], [$lt.eq qty(0.014, "ppm per hour", per: "/")$], [Bandwidth], [DC to $qty(20, "kHz")$], [Drift-free operation], [$qty(30, "day")$], ), @@ -1087,10 +1090,10 @@ continuous computation. ==== Drift rate and long-term stability <drift-rate-and-long-term-stability> -The drift rate specification of $qty(0.014, "ppm per hour")$ means: +The drift rate specification of $qty(0.014, "ppm per hour", per: "/")$ means: $ - dv(epsilon, t) lt.eq num("0.014e-6") times qty(20, "volt per hour") = qty(280, "nano volt per hour") + dv(epsilon, t) lt.eq num("0.014e-6") times qty(20, "volt per hour", per: "/") = qty(280, "nano volt per hour", per: "/") $ Over 30 days (720 hours), the accumulated drift is: @@ -1102,7 +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 - $qty(0.014, "ppm per hour")$. After 15 days, it reaches $qty(10, "ppm")$ total + $qty(0.014, "ppm per hour", per: "/")$. 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 $t = 0$. @@ -1190,7 +1193,7 @@ absolute temperature $T$ is: $ e_n = sqrt(4 k_B T R) $ Where: -- $k_B = qty("1.381e-23", "joule per kelvin")$ (Boltzmann constant), +- $k_B = qty("1.381e-23", "joule per kelvin", per: "/")$ (Boltzmann constant), - $T =$ absolute temperature ($unit(K)$), - $R =$ resistance ($unit("ohm")$). @@ -1402,7 +1405,7 @@ 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 -$qty(-20, "decibel per decade")$, high-frequency supply ripple poses a +$qty(-20, "decibel per decade", per: "/")$, high-frequency supply ripple poses a significantly greater threat to precision than DC supply variations. ====== Mathematical model <power-supply-noise-coupling-mathematical-model> |