@Muse - Connecting the logarithmic converter stage directly to its topological antilogarithmic opposite through their shared reference ground node forms a complete computational identity pipeline:
$$\text{Input } \longrightarrow \ln(x) \longrightarrow \exp(\ln(x)) \longrightarrow \text{Output } (\approx x)$$
### Circuit Topology
- **Logarithmic Stage (Left):**
- #Vin provides a time-varying positive voltage at #in.
- Resistor #R1 feeds current $I_{\text{in}} = \frac{V_{\text{in}}}{R_1}$ into the virtual ground node of #OA1.
- Diode #D1 acts as the feedback impedance, generating the logarithmic compression:
$$V_{\text{log}} = -n V_T \ln\left(\frac{V_{\text{in}}}{I_S R_1}\right)$$
- **Antilogarithmic Stage (Right):**
- Node #log drives the cathode of input diode #D2.
- Because #OA2 holds its inverting input at virtual ground, the voltage drop across #D2 is $-V_{\text{log}}$, exactly recreating an exponential current equal to $I_{\text{in}}$.
- Feedback resistor #R2 converts this current back into a linear voltage at #out:
$$V_{\text{out}} = R_2 I_S \exp\left(\frac{-V_{\text{log}}}{n V_T}\right) = \frac{R_2}{R_1} V_{\text{in}} = V_{\text{in}}$$
### Oscilloscope View
- **Blue trace (#in):** Original input signal ($1\text{ V}$ to $9\text{ V}$).
- **Green trace (#log):** Compressed logarithmic signal at the junction ($-0.72\text{ V}$ to $-0.66\text{ V}$).
- **Orange trace (#out):** Fully reconstructed linear replica ($1\text{ V}$ to $9\text{ V}$), demonstrating reversible analog computation across electron transitions.
