Varactor Diode

1. Theory

• Definition: A varactor (varicap) diode is a reverse-biased PN or Schottky junction used as a voltage-controlled capacitor.
• Depletion capacitance: The depletion region acts as the capacitor dielectric, and its width, and so the capacitance, changes with reverse voltage.
• Grading coefficient: The doping profile sets how strongly capacitance varies with voltage: $m=1/2$ for abrupt, $m=1/3$ for linearly graded and up to about $m=2$ for hyperabrupt junctions.
• Hyperabrupt profile: Doping that falls away from the junction gives a steep C-V curve and a nearly linear frequency-voltage tuning law in an LC tank.
• Series resistance: Undepleted bulk and contact resistance set the quality factor $Q$ and the cutoff frequency.

2. Working Principle

• Reverse bias: Increasing reverse voltage widens the depletion region and lowers the capacitance; decreasing it raises the capacitance.
• No DC current: Only a tiny leakage flows, so the tuning voltage source supplies almost no power.
• Tuning range: The capacitance ratio over the bias range is set by the grading coefficient and the voltage span.
• Resonant tuning: In an LC tank, the resonant frequency follows $1/\sqrt{L{C}_j(V)}$, so the bias voltage tunes the frequency.
• High-frequency loss: $Q$ falls inversely with frequency because of series resistance, limiting the usable frequency.
• Nonlinear reactance: The voltage-dependent capacitance generates harmonics under large RF drive, which is used for frequency multiplication.

3. Applications

• Voltage-controlled oscillators: Tuning element in PLL synthesizers for radios, phones and TV tuners.
• Electronically tuned filters: Tunable RF filters and matching networks.
• mm-wave and THz frequency multipliers: Schottky varactor multipliers are the standard compact sources above about 100 GHz.

Name	Formula	Related Formulae	Variables/Constants
Depletion capacitance (voltage-tuning law)	$C_j(V)=\frac{C_{j0}}{(1+V/V_{bi}{)}^m}$	$C_{j0}=\frac{{\epsilon }_{s}A}{W_0}\text{(see PN Junction Diode page)}$	$\begin{array}{r}{C}_j(V):depletioncapacitanceasa\\ functionofreversebias\end{array}$ $C_{j0}:zero-biascapacitance$ $m:gradingcoefficient$
Grading coefficient vs. doping profile	$m=\frac{1}{2+a}$	$N(x)=N_0{x}^a$ $m=\frac{1}{2}(abrupt,a=0);m=\frac{1}{3}(linearlygraded,a=1);m=2(hyperabrupt,a=-\frac{3}{2})$	$a:exponentofthedopingprofileN(x)$
Capacitance tuning ratio	$\frac{C_{max}}{C_{min}}={\left(\frac{V_{bi}+V_{max}}{V_{bi}+V_{min}}\right)}^m$		$\begin{array}{r}{C}_{max},C_{min}:capacitanceatthe\\ minimumandmaximumreversebiasofthe\\ tuningrange\end{array}$
Cutoff frequency	$f_c=\frac{1}{2\pi R_s{C}_j}$		$f_c:figure-of-meritcutofffrequency$ $R_s:parasiticseriesresistance$
Quality factor	$Q=\frac{1}{\omega R_s{C}_j}$	$Q=\frac{f_c}{f}$	$\begin{array}{r}Q:qualityfactoratoperatingangular\\ frequency\omega \end{array}$ $f:operatingfrequency$
Resonant frequency (VCO tank circuit)	$f_{res}(V)=\frac{1}{2\pi \sqrt{L{C}_j(V)}}$		$\begin{array}{r}{f}_{res}(V):tankresonantfrequencyasa\\ functionoftuningvoltage\end{array}$ $L:fixedinductanceoftheresonanttank$

Important Questions

Ques: Why would a hyperabrupt junction ($m=2$) be preferred over a standard abrupt junction ($m=0.5$) for a voltage-controlled oscillator?

A VCO’s resonant frequency depends on capacitance as $f_{res}\propto 1/\sqrt{C_j(V)}$, and since a standard abrupt junction gives $C_j\propto (V_{bi}+V{)}^{-1/2}$, the resulting tuning characteristic $f_{res}(V)$ is nonlinear and difficult to control precisely across a loop (e.g. a PLL). A hyperabrupt profile, engineered with doping decreasing away from the junction ($a=-3/2$), produces $C_j\propto (V_{bi}+V{)}^{-2}$, and substituting this into the resonant-frequency formula gives $f_{res}\propto \sqrt{(V_{bi}+V{)}^2}=(V_{bi}+V)$ — a directly linear relationship between tuning voltage and oscillator frequency. This linearization is specifically why hyperabrupt varactors are deliberately manufactured for VCO applications despite being more difficult to fabricate than a simple abrupt junction. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why does series resistance limit varactor performance so strongly at high frequency?

Every real varactor has some parasitic series resistance from the undepleted bulk semiconductor, substrate, and ohmic contacts in series with the tuning capacitance. Quality factor $Q=1/(\omega R_s{C}_j)$ shows this resistance’s effect scales directly with frequency, so even a small $R_s$ that is negligible at low frequency becomes the dominant loss mechanism as $\omega$ increases — degrading the sharpness (selectivity) of any resonant circuit the varactor tunes and ultimately setting the practical upper frequency limit, $f_c$, beyond which the device behaves more like a lossy resistor than a usable variable reactance. This is why varactor datasheets specify $Q$ at a stated test frequency rather than as a single frequency-independent number. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Related pages in this vault: MOS Varactors, PN Junction, Step Recovery Diode, PIN Diode, Schottky Diode, Impact Ionization Avalanche Transit Time (IMPATT) Diode, RF MEMS Passives, Microwave Diodes (IMPATT, Gunn, Limiter, Mixer, Tunnel, Varactor).