add shertz (square hertz) custom unit

1 files changed, 27 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 $qty(20, "kHz")$:
 
 $