Negative Resistance
Understanding Negative Resistance
In a normal resistor, current increases with voltage (Ohm's law, positive resistance). In a negative resistance device, there is a region of the I-V curve where increasing voltage causes decreasing current. The slope dV/dI is negative, hence the name. This means the device converts DC bias power into AC power: the AC voltage and current are 180 degrees out of phase, so the device acts as a source of RF energy rather than a sink.
When a negative resistance device is placed inside a resonant structure (waveguide cavity, microstrip resonator, or dielectric resonator), it compensates the cavity's inherent resistive losses. If the magnitude of the negative resistance exceeds the total positive resistance (cavity loss plus external load), oscillation starts spontaneously and builds until nonlinear saturation limits the amplitude. The oscillation frequency is set by the cavity's resonant frequency, while the output power is determined by the device's I-V characteristics and the circuit's coupling to the external load.
Oscillation Conditions
|Zdevice| > |Zcircuit| (magnitude of negative R exceeds circuit loss)
AND Im{Zdevice} + Im{Zcircuit} = 0 (resonance condition)
Reflection Coefficient Form:
|Γin| × |ΓL| ≥ 1 (loop gain exceeds unity)
Negative Resistance Power Delivery:
PAC = ½ |I|² |Rneg| (power delivered to the circuit)
Steady-State Output Power:
Pout = ηDC-RF × VDC × IDC
Typical η: 5-15% (Gunn), 15-25% (IMPATT), 1-3% (Tunnel)
Negative Resistance Diode Comparison
| Device | Mechanism | Frequency Range | Power (CW) | Efficiency | Noise |
|---|---|---|---|---|---|
| Gunn Diode | Transferred electron (GaAs/InP) | 1 to 200 GHz | 10 mW to 1 W | 5-15% | Low (−120 dBc/Hz) |
| IMPATT Diode | Avalanche + transit time | 3 to 300 GHz | 100 mW to 10 W | 15-25% | High (−100 dBc/Hz) |
| Tunnel Diode | Quantum tunneling | DC to 100+ GHz | < 10 mW | 1-3% | Very low |
| Transistor (biased for NDR) | Feedback via S12 | DC to fT | mW to W | Varies | Low |
Frequently Asked Questions
How does a negative resistance device generate RF power?
When a device has negative differential resistance, AC voltage and current are 180 degrees out of phase, so the device delivers energy to the circuit rather than absorbing it. Embedded in a resonant cavity, the negative resistance compensates the cavity's positive resistance losses. If the negative resistance magnitude exceeds the total cavity loss, oscillation builds up and sustains at the resonant frequency. The DC bias provides the energy source; the negative resistance mechanism converts DC to RF.
What are the main types of negative resistance diodes at microwave frequencies?
Gunn diodes use the transferred electron effect in GaAs or InP, operating from 1 to 200 GHz with 10 mW to 1 W output and low phase noise. IMPATT diodes use avalanche breakdown and carrier transit time for the highest solid-state oscillator power (up to 10 W CW at X-band, 3 to 300 GHz) but with higher noise. Tunnel diodes use quantum mechanical tunneling for NDR at DC to 100+ GHz but with very low power (< 10 mW). Each fills a different niche in the frequency-power-noise trade space.
What is the connection between negative resistance and amplifier instability?
A transistor with feedback through S12 can present negative resistance at its input or output when certain source or load impedances are applied. This is unwanted oscillation. Stability analysis (K-factor, mu parameter) checks whether any passive termination can trigger this condition. If |Γin| > 1, the port has negative resistance and will oscillate at the frequency where the resonance condition is satisfied. This is why stability must be verified from DC through fT, not just at the design frequency.