Negative-Resistance Oscillator
A one-port oscillator uses an active device that presents a negative resistance (Rin < 0, so |Γin| > 1) over the band of interest. Sustained oscillation requires the load to satisfy ΓinΓL = 1, which is equivalent to ZL = −Zin: the load resistance cancels the device's negative resistance and the load reactance cancels its reactance. This tool computes the reflection coefficients, the sustaining load, and the small-signal start-up margin.
Equations & Parameters ▸
\(\Gamma_{in}=\dfrac{Z_{in}-Z_0}{Z_{in}+Z_0},\quad |\Gamma_{in}|>1\) for a negative-resistance device.
Oscillation: \(\Gamma_{in}\Gamma_L=1\ \Longleftrightarrow\ Z_L=-Z_{in}\), i.e. \(R_L=-R_{in},\ X_L=-X_{in}\).
Start-up (small signal): \(R_L+R_{in}(0)<0\); a common design point is \(R_L=\tfrac{1}{3}|R_{in}(0)|\) so |Rin| falls to RL as the amplitude grows.
Oscillation: \(\Gamma_{in}\Gamma_L=1\ \Longleftrightarrow\ Z_L=-Z_{in}\), i.e. \(R_L=-R_{in},\ X_L=-X_{in}\).
Start-up (small signal): \(R_L+R_{in}(0)<0\); a common design point is \(R_L=\tfrac{1}{3}|R_{in}(0)|\) so |Rin| falls to RL as the amplitude grows.
| Rin | Device input resistance (Ω) — enter a negative value. |
| Xin | Device input reactance (Ω) at the oscillation frequency. |
| Z0 | Reference impedance for the reflection coefficients. |
| f | Oscillation frequency (GHz, informational). |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., §13.3.
Inputs
Ω
< 0Ω
ReactanceΩ
ReferenceGHz
OptionalResults
Device (one-port)
Zin—
Γin—
Negative-R present?—
Sustaining load
ZL = −Zin—
ΓL—
Check |ΓinΓL|—
Start-up guideline
RL for oscillation—
Design point RL ≈ |Rin|/3—
One-port oscillator