Adding Bode's noise theorem

content/_app_millers_theorem.qmd → content/_app_circuit_theorems.qmd

@@ -14,7 +14,9 @@ See the License for the specific language governing permissions and
 limitations under the License.
 :::
 
-# Appendix: Miller's Theorem {#sec-miller-theorem}
+# Appendix: Useful Circuit Theorems
+
+## Miller's Theorem {#sec-miller-theorem}
 
 Using Miller's theorem we can find the equivalent circuit of an impedance connected between two nodes, and we know the transfer function between these nodes. The given situation is shown in @fig-miller-theorem, and the equivalent circuit is shown in @fig-miller-theorem-equivalent.
 
@@ -34,3 +36,15 @@ to arrive at an equivalent circuit, given that $A = V_\mathrm{B} / V_\mathrm{A}$
 Note that if $V_\mathrm{A} = V_\mathrm{B}$ then there is no current flow through $Z$, and accordingly the impedances $Z_1 = Z_2 = \infty$.
 
 Miller's theorem can be quite handy when an impedance is strapped between two nodes, and we want to break this connection in a calculation, e.g., considering the effect of $\CGD$ in a MOSFET.
+
+## Bode's Noise Theorem {#sec-bode-noise-theorem}
+
+The total integrated noise of any (no matter how complicated) $RLC$ network (interpreted as a one-port) is given by
+
+$$
+\overline{V_\mathrm{n}^2} = kT \left( \frac{1}{C_\infty} - \frac{1}{C_0} \right),
+$$
+
+where $C_\infty$ is the capacitance looking into the network with all resistors and inductors open-circuited, and $C_0$ is the capacitance looking into the circuit when all inductors and resistors are shorted [@Pavan_2019].
+
+Reference [@Pavan_2019] is an excellent read deriving Bode's noise theorem from different angles.

content/_sec_mosfet_diode.qmd

@@ -240,6 +240,8 @@ which is independent of $R$! This is a surprising result, and is the well-known
 Intuitively, we could argue that the noise increases with larger $R$, but at the same time, the bandwidth decreases and therefore $R$ does not add additional noise.
 
 Side note: The shortest derivation of this formula involves the [equipartition theorem](https://en.wikipedia.org/wiki/Equipartition_theorem): Any system in thermal equilibrium has an energy of $kT/2$ per degree of freedom. This $RC$ system has one degree of freedom in the capacitor, and the stored energy in the capacitor is $CV_\mathrm{rms}^2/2$. Equating both energies we find that $V_\mathrm{rms}^2 = kT/C$.
+
+To calculate the total output noise of a generalized passive network Bode's noise theorem is quite practical (see @sec-bode-noise-theorem).
 :::
 
 Calculating the rms noise voltage for our MOSFET diode we get

index.qmd

@@ -52,7 +52,7 @@ To be added in a future release.
 
 {{< include /content/_sec_summary.qmd >}}
 {{< include /content/_app_middlebrook_method.qmd >}}
-{{< include /content/_app_millers_theorem.qmd >}}
+{{< include /content/_app_circuit_theorems.qmd >}}
 {{< include /content/_app_voltage_buffer_zout.qmd >}}
 {{< include /content/_app_linux_cheatsheet.qmd >}}
 {{< include /content/_app_xschem_cheatsheet.qmd >}}

references.bib

@@ -1,13 +1,39 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% https://bibdesk.sourceforge.io/
 
-%% Created for Harald Pretl at 2024-12-17 15:44:34 +0100 
+%% Created for Harald Pretl at 2024-12-28 16:40:00 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@article{Pavan_2019,
+	author = {Pavan, Shanthi},
+	date-added = {2024-12-28 13:28:11 +0100},
+	date-modified = {2024-12-28 13:28:24 +0100},
+	doi = {10.1109/TCSII.2019.2907860},
+	journal = {IEEE Transactions on Circuits and Systems II: Express Briefs},
+	number = {5},
+	pages = {738-742},
+	title = {An Alternative Approach to Bode's Noise Theorem},
+	volume = {66},
+	year = {2019},
+	bdsk-url-1 = {https://doi.org/10.1109/TCSII.2019.2907860}}
+
+@article{Sing_2024,
+	author = {Singh, Chandan Kumar and Temes, Gabor C},
+	date-added = {2024-12-28 13:09:51 +0100},
+	date-modified = {2024-12-28 13:10:10 +0100},
+	doi = {10.1109/mcas.2024.3462661},
+	journal = {IEEE Circuits and Systems Magazine},
+	number = {4},
+	pages = {65--69},
+	title = {{R-C Ladder Design: A Tutorial [CAS Education]}},
+	volume = {24},
+	year = {2024},
+	bdsk-url-1 = {https://doi.org/10.1109/mcas.2024.3462661}}
+
 @misc{Blumlein_1937,
 	author = {A. D. {Blumlein}},
 	date-added = {2024-12-17 15:24:07 +0100},
@@ -26,7 +52,8 @@ @article{Widlar_1965
 	pages = {586--590},
 	title = {{Some Circuit Design Techniques for Linear Integrated Circuits}},
 	volume = {12},
-	year = {1965}}
+	year = {1965},
+	bdsk-url-1 = {https://doi.org/10.1109/tct.1965.1082512}}
 
 @article{Neag_2015,
 	author = {Neag, Marius and One{\c t}, Raul and Kov{\'a}cs, Istv{\'a}n and M{\u a}rtari, Paul},