diff options
| -rw-r--r-- | module-design.typ | 47 | ||||
| -rw-r--r-- | preamble.typ | 1 |
2 files changed, 28 insertions, 20 deletions
diff --git a/module-design.typ b/module-design.typ index db968a1..f30c9fc 100644 --- a/module-design.typ +++ b/module-design.typ @@ -230,15 +230,15 @@ operators. table( columns: 3, table.header([Symbol], [Definition], [Typical unit]), - [$e_n$], [Voltage noise spectral density], [$unit("nV")/sqrt(unit("Hz"))$], + [$e_n$], [Voltage noise spectral density], [$unit("nano volt per shertz", per: "/")$], [$upright(i)_n$], [Current noise spectral density], - [$unit("pA")/sqrt(unit("Hz"))$ or $unit("fA")/sqrt(unit("Hz"))$], + [$unit("pico ampere per shertz", per: "/")$ or $unit("femto ampere per shertz", per: "/")$], - [$e_(n,"white")$], [White noise component], [$unit("nV")/sqrt(unit("Hz"))$], + [$e_(n,"white")$], [White noise component], [$unit("nano volt per shertz", per: "/")$], - [$e_(n,1/f)$], [$1/f$ noise component], [$unit("nV")/sqrt(unit("Hz"))$ at $qty(1, "Hz")$], + [$e_(n,1/f)$], [$1/f$ noise component], [$unit("nano volt per shertz", per: "/")$ at $qty(1, "Hz")$], [$f_c$], [Noise corner frequency ($1/f$ to white)], [$unit("Hz")$], @@ -285,7 +285,7 @@ operators. [$accent(Q, dot)$], [Heat flux], [$unit("W")$], [$accent(m, dot)$], [Mass flow rate], [$unit("kilo gram per second", per: "/")$], - [$c_p$], [Specific heat capacity], [$unit("J")/(unit("kg") unit("K"))$], + [$c_p$], [Specific heat capacity], [$unit("J")/(unit("kg") dot unit("K"))$], ), caption: [Thermal quantities], ) <table-thermal-quantities> @@ -1134,7 +1134,7 @@ $ For a single-pole system with gain-bandwidth product $upright("GBW")$ and DC closed-loop gain $G$: -$ A(f)/A(0) gt.eq 1/sqrt(1 + (f times G/upright("GBW"))^2) $ +$ A(f)/A(0) gt.eq 1/sqrt(1 + (f G/upright("GBW"))^2) $ Solving for $qty(10, "ppm")$ gain error at $qty(20, "kHz")$ with $G = 1$ (unity gain buffer): @@ -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 $unit("nV")/sqrt(unit("Hz"))$: +$e_n (f)$ in $unit("nano volt per shertz", per: "/")$: $ e_n (f) = sqrt(e_(n,"white")^2 + (e_(n,1/f)^2)/f) = e_(n,"white") sqrt(1 + f_c/f) @@ -1290,22 +1290,28 @@ servo loop. table( columns: 4, table.header([Op-amp class], [$e_(n,"white")$], [$f_c$], [Notes]), - [General purpose (TL07x)], [$18 unit("nV")/sqrt(unit("Hz"))$], [$qty(200, "Hz")$], [JFET input], + [General purpose (TL07x)], [$18 unit("nano volt per shertz", per: "/")$], [$qty(200, "Hz")$], [JFET input], - [Low noise (OPA211)], [$1.1 unit("nV")/sqrt(unit("Hz"))$], [$qty(10, "Hz")$], [Bipolar input], + [Low noise (OPA211)], [$1.1 unit("nano volt per shertz", per: "/")$], [$qty(10, "Hz")$], [Bipolar input], - [Precision low noise (LT1028)], [$0.85 unit("nV")/sqrt(unit("Hz"))$], [$qty(3.5, "Hz")$], [Bipolar input], + [Precision low noise (LT1028)], + [$0.85 unit("nano volt per shertz", per: "/")$], + [$qty(3.5, "Hz")$], + [Bipolar input], - [Chopper stabilized (LTC2057)], [$7 unit("nV")/sqrt(unit("Hz"))$], [$lt qty(1, "Hz")$], [No $1/f$ corner], + [Chopper stabilized (LTC2057)], + [$7 unit("nano volt per shertz", per: "/")$], + [$lt qty(1, "Hz")$], + [No $1/f$ corner], ), caption: [Op-amp voltage noise typical magnitudes], ) <table-opamp-voltage-noise-typical-magnitude> -For a precision op-amp ($1 unit("nV")/sqrt(unit("Hz")), f_c = qty(10, "Hz")$) +For a precision op-amp ($1 unit("nano volt per shertz", per: "/"), f_c = qty(10, "Hz")$) over $qty(0.001, "Hz")$ to $qty(20, "kHz")$: $ - V_(n,"rms") & = sqrt((num("1e-9"))^2 times 20000 + (num("1e-9"))^2 times 10 times ln(20000/0.001)) \ + V_(n,"rms") & = sqrt((num("1e-9"))^2 times 20000 + (num("1e-9"))^2 times 10 ln(20000/0.001)) \ V_(n,"rms") & = sqrt(num("2e-14") + num("1.68e-13")) = sqrt(num("1.88e-13")) approx qty(0.43, "uVrms") $ @@ -1314,14 +1320,14 @@ $ Op-amp voltage noise appears directly at the input and is gained by the closed-loop gain: -$ V_(n,"out") = e_n times (1+R_f/R_"in") $ +$ V_(n,"out") = e_n (1+R_f/R_"in") $ For a unity-gain buffer ($R_f = 0$), $V_(n,"out") = e_n$. For a gain-of-10 amplifier, output noise is $10 times$ input voltage noise. ====== Compensation strategy <opamp-voltage-noise-compensation-strategy> -- Select low noise bipolar op-amps ($e_n < 2 unit("nV")/sqrt(unit("Hz"))$) for +- Select low noise bipolar op-amps ($e_n < 2 unit("nano volt per shertz", per: "/")$) for low-source-impedance nodes, - Minimize closed-loop gain stages in initial processing stages, - Use chopper-stabilized amplifiers where $1/f$ where drift dominates @@ -1340,7 +1346,7 @@ due to their extremely low bias currents. ====== Mathematical model <opamp-current-noise-mechanical-model> -Current noise spectral density $i_n$ in $unit("pA")/sqrt(unit("Hz"))$ flows +Current noise spectral density $i_n$ in $unit("pico ampere per shertz", per: "/")$ flows through the source impedance $Z_"source"$ seen by the op-amp terminal, generating an equivalent input voltage noise: @@ -1356,15 +1362,16 @@ $ 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)], [$1 unit("pA")/sqrt(unit("Hz"))$], [Low voltage noise, moderate current noise], + [Bipolar (LT1028)], [$1 unit("pico ampere per shertz", per: "/")$], [Low voltage noise, moderate current noise], - [JFET (OPA627)], [$2.5 unit("fA")/sqrt(unit("Hz"))$], [Negligible], - [CMOS (LMC6001)], [$0.13 unit("fA")/sqrt(unit("Hz"))$], [Negligible], + [JFET (OPA627)], [$2.5 unit("femto ampere per shertz", per: "/")$], [Negligible], + + [CMOS (LMC6001)], [$0.13 unit("femto ampere per shertz", per: "/")$], [Negligible], ), caption: [Op-amp current noise typical magnitudes], ) <table-opamp-current-noise-typical-magnitude> -For a bipolar op-amp ($1 unit("pA")/sqrt(unit("Hz"))$) with $qty(10, "kilo ohm")$ +For a bipolar op-amp ($1 unit("pico ampere per shertz", per: "/")$) with $qty(10, "kilo ohm")$ source impedance over $qty(20, "kHz")$: $ diff --git a/preamble.typ b/preamble.typ index 5823a54..597317e 100644 --- a/preamble.typ +++ b/preamble.typ @@ -17,6 +17,7 @@ #add-unit("volt DC", "VDC", "V_\"DC\"") #add-unit("uVrms", "uVrms", "mu V_\"rms\"") #add-unit("decade", "dec", "upright(\"dec\")") +#add-unit("shertz", "sHz", "sqrt(upright(\"Hz\"))") #set document( title: [SAME Analog Modular Ecosystem], |