Theory finished, next is actual design

.vscode/settings.json

@@ -1,19 +1,24 @@
 {
     "cSpell.words": [
+        "Banba",
         "cmim",
         "CMRR",
+        "CTAT",
         "gmgds",
         "loopgain",
         "openloop",
         "OSIC",
         "PSRR",
+        "PTAT",
         "quasistatic",
+        "Razavi",
         "rhigh",
         "rppd",
         "rsil",
         "stronginversion",
         "techsweep",
         "vdsat",
-        "weakinversion"
+        "weakinversion",
+        "Widlar"
     ]
 }

content/_sec_biasing.qmd

@@ -172,7 +172,7 @@ plt.grid(True)
 
 A well described design of a Banba bandgap reference (including a two-stage OTA and a regulated cascode for the output current mirror), covering much more details than discussed here, can be found in [Razavi_2021_bandgap].
 
-::: {.callout-tip title="Exercise: Improved Low-Voltage Bandagap"}
+::: {.callout-tip title="Exercise: Improved Low-Voltage Bandgap"}
 As an *optional* exercise for advanced users: Design a bandgap circuit following [Razavi_2021_bandgap]. Implement the shown two-stage OTA and the regulated cascode.
 
 As a starting point, the design of @sec-banba-bandgap can be used. As this design will contain more blocks, please build up a hierarchical design, with the OTAs designed in separate subcircuits.

content/_sec_differential_ota.qmd

@@ -148,3 +148,13 @@ In summary, stability investigations are critically important for differential c
 Instead of a common-mode regulation loop (and all its complications regarding stability) often a common-mode setting is sufficient (after all, a somewhat imprecise setting of the dc points is good enough). A common-mode setting has the advantage that no error amplifier is required. We will also use this approach of a common-mode loop setting in the adapted differential OTA shown in @fig-diff-ota-resload-miller-cm.
 
 {{< include ./figures/_fig_ota_diff_twostage_miller_cm.qmd >}}
+
+Resistors $R_{3,4}$ sense the output voltages and create a replica of the common-mode point (assuming $R_3 = R_4$). This common-mode point is connected to the gates of $M_{7,8}$ to essentially connect $M_{7,8}$ like a diode (only for common-mode operation); in differential mode, $M_7$ and $M_8$ act as current source, like the load of the differential pair $M_{3,5}$. However, since we want to set the common-mode voltage at the output independently from $\VGS[7,8]$ we also pull a current through $R_{3,4}$ to cause $\VDS[7,8] \neq \VGS[7,8]$; essentially, this is a diode connection including a voltage shift! The output common-mode voltage is then given by
+
+$$
+V_\mathrm{out,cm} = \VGS[7,8] + \frac{R_{3,4} \ID[11]}{2}.
+$$
+
+::: {.callout-warning title="Modify Bias Points with Currents"}
+Keep the technique shown in @fig-diff-ota-resload-miller-cm (using $R_{3,4}$ and $M_{11}$) in mind: You can always modify a bias point by injecting a dc current into a node, or by pulling a dc current out of a node (or do both to increase or lower the quiescent current through a resistor or transistor)! Since we likely have already current mirrors in the circuit it is usually a minor effort adding MOSFETs to create these bias currents.
+:::

figures/_fig_ota_diff_twostage_miller_cm.qmd

@@ -27,29 +27,29 @@ with sd.Drawing(canvas='svg') as d:
     
     M1 = elm.AnalogNFet(offset_gate=False).drop('source').theta(0).label('$M_1$', ofst=-1.5).reverse()
     elm.Line().down().length(0.5)
-    elm.Line().right().length(2).dot()
+    elm.Line().right().length(0.5).dot()
     d.push()
 
-    elm.Line().down().length(1.5)
+    elm.Line().down().length(4.5)
     M10 = elm.AnalogNFet(offset_gate=False).anchor('drain').theta(0).label('$M_{10}$', ofst=-1.5).reverse()
     elm.Ground()
     elm.Line().left().length(0.5).at(M10.gate)
-    elm.Line().up().length(1).dot()
+    elm.Line().up().length(1)
     pos3 = d.here
     elm.Line().left().length(7.5)
     d.push()
     elm.Line().down().length(1)
     elm.Line().left().length(0.5)
     M9 = elm.AnalogNFet(offset_gate=False).anchor('gate').theta(0).label('$M_9$')
     elm.Ground()
-    elm.Line().up().length(6).at(M9.drain)
+    elm.Line().up().length(8.5).at(M9.drain)
     Ibias = elm.SourceI().up().label(r'$I_\mathrm{bias}$').reverse()
     elm.Vdd()
     d.pop()
     elm.Line().left().tox(M9.drain).idot().dot()
 
     d.pop()
-    elm.Line().right().length(2)
+    elm.Line().right().length(3.5)
     elm.Line().up().length(0.5)
     M2 = elm.AnalogNFet(offset_gate=False).anchor('source').theta(0).label('$M_2$')
     
@@ -90,14 +90,11 @@ with sd.Drawing(canvas='svg') as d:
     elm.Capacitor().right().label(r'$C_\mathrm{m1}$')
     elm.Resistor().right().label(r'$R_\mathrm{m1}$').tox(M3.drain).dot()
     d.pop()
-    elm.Line().down().toy(M10.drain)
-    M7 = elm.AnalogNFet(offset_gate=False).anchor('drain').theta(0).label('$M_7$', ofst=-1.5).reverse()
+    elm.Line().down().length(4.5)
+    M7 = elm.AnalogNFet(offset_gate=False).anchor('drain').theta(0).label('$M_7$')
     elm.Ground().at(M7.source)
-    elm.Line().at(M7.gate).left().length(0.5)
-    elm.Line().up().length(1).dot()
 
     elm.Line().at(M6.drain).down().length(0.5)
-    #elm.Dot().label("$B'$", 'left')
     elm.Dot()
     d.push()
     d.push()
@@ -109,9 +106,10 @@ with sd.Drawing(canvas='svg') as d:
     elm.Line().down().toy(M7.drain)
     M8 = elm.AnalogNFet(offset_gate=False).anchor('drain').theta(0).label('$M_8$', ofst=-1.5).reverse()
     elm.Ground().at(M8.source)
-    elm.Line().at(M8.gate).left().length(0.5)
-    elm.Line().up().length(1)
-    elm.Line().left().length(6.5)
+    elm.Line().at(M8.gate).left().tox(M2.source)
+    elm.Line().left().length(0.5).dot()
+    pos4 = d.here
+    elm.Line().at(M8.gate).left().tox(M7.gate)
 
     d.here = pos1
     R1 = elm.Resistor().right().label('$R_1$').dot()
@@ -124,4 +122,19 @@ with sd.Drawing(canvas='svg') as d:
     elm.Line().left().to(M3.gate)
     d.pop()
     elm.Line().right().to(M5.gate)
+
+    elm.Line().up().length(0.5).at(M7.drain)
+    elm.Resistor().right().tox(pos4).idot().dot().label('$R_3$')
+    d.push()
+    elm.Line().down().toy(M7.gate)
+    pos5 = d.here
+    d.pop()
+    elm.Resistor().right().tox(M8.drain).dot().label('$R_4$')
+
+    elm.Line().down().at(pos5).toy(M10.drain)
+    M11 = elm.AnalogNFet(offset_gate=False).anchor('drain').theta(0).label('$M_{11}$', ofst=-1.5).reverse()
+    elm.Ground()
+    elm.Line().left().length(0.5).at(M11.gate)
+    elm.Line().up().length(1)
+    elm.Line().left().length(3).dot()
 ```