Clapp Oscillator

When a Colpitts oscillator is not stable enough at high frequencies, engineers add a third capacitor in series with the inductor. This modification is the Clapp oscillator, and it achieves significantly better frequency stability than a standard Colpitts by isolating the tank circuit from the transistor's variable junction capacitance. VHF synthesizers and precision signal generators use this topology.

Core Concept

The Clapp oscillator is a modified Colpitts oscillator. A third capacitor C3 is inserted in series with the inductor L. This creates a three-element series LC branch (L, C3 in series) which resonates with the parallel combination of C1 and C2. Because C3 is much smaller than C1 or C2, it dominates the series equivalent capacitance.

The key improvement is frequency stability. In a standard Colpitts, C1 and C2 are directly connected to the transistor's collector and emitter. The transistor's junction capacitances (Cbe, Cce) are in parallel with C1 and C2. These junction capacitances vary with temperature and bias current, shifting the oscillation frequency.

In the Clapp, C1 and C2 are made large (typically 1 nF or more) so that the transistor's junction capacitances (a few picofarads) represent a very small fraction of C1 and C2. The small C3 (10 pF) controls the frequency. Since C3 is physically separate from the transistor, it is much less affected by transistor parameter variations. The result is a frequency stability 5 to 10 times better than Colpitts.

Key Equations

Effective series capacitance of the tank:

1/Ceq = 1/C1 + 1/C2 + 1/C3 Since C1 and C2 are much larger than C3, Ceq ≈ C3.

Oscillation frequency (approximate):

f0 ≈ 1 / (2π × sqrt(L × C3)) This approximation is valid when C3 << C1 and C3 << C2.

Exact oscillation frequency:

f0 = 1 / (2π × sqrt(L × Ceq)) where Ceq = 1/(1/C1 + 1/C2 + 1/C3).

Given:
  L = 2 µH = 2 × 10^-6 H
  C1 = 1 nF = 1000 pF (large, sets feedback)
  C2 = 1 nF = 1000 pF (large, sets feedback)
  C3 = 10 pF = 10 × 10^-12 F (small, controls frequency)

Why this formula:
  C3 << C1 and C3 << C2, so Ceq ≈ C3. Use approximate formula.

Formula:
  Ceq = 1 / (1/C1 + 1/C2 + 1/C3)

Substitution:
  1/Ceq = 1/1000pF + 1/1000pF + 1/10pF
        = 0.001 + 0.001 + 0.1 (all in pF^-1 × 10^0 units)
        = 0.102 pF^-1
  Ceq = 1/0.102 = 9.80 pF ≈ 10 pF (confirms C3 dominates)

  f0 = 1 / (2π × sqrt(L × Ceq))
     = 1 / (2π × sqrt(2 × 10^-6 × 9.80 × 10^-12))
     = 1 / (2π × sqrt(1.96 × 10^-17))
     = 1 / (2π × 1.4 × 10^-8.5)
     = 1 / (2π × 1.4 × 10^-8.5)

Calculation:
  sqrt(1.96 × 10^-17) = 1.4 × 10^-8.5 = 4.43 × 10^-9
  f0 = 1 / (2π × 4.43 × 10^-9)
     = 1 / (2.784 × 10^-8)
     = 35.9 × 10^6 Hz

Final Answer:
  f0 ≈ 35.9 MHz
  Transistor junction capacitance (~2 pF) is only 0.2% of C1, causing negligible frequency error.

Exam Tip: GATE questions on Clapp oscillators focus on two points. First, the frequency is approximately 1/(2π sqrt(LC3)) because C3 is smallest and dominates Ceq. If you use 1/(2π sqrt(L(C1||C2||C3))) you get a nearly identical answer since C3 dominates, but you must show Ceq calculation. Second, the reason Clapp is more stable than Colpitts is that C1 and C2 are large, so transistor junction capacitance changes are a tiny fraction of them and barely shift frequency.

Key Properties

• The Clapp is a Colpitts with a third capacitor C3 added in series with L. This makes Ceq ≈ C3 when C3 << C1 and C3 << C2.
• Frequency stability is 5 to 10 times better than Colpitts because transistor junction capacitances are negligible compared to large C1 and C2.
• C1 and C2 (typically 1 nF) determine the feedback fraction β = C1/(C1+C2). Their large value provides stable feedback.
• C3 (typically 10 to 100 pF) controls the oscillation frequency. Making C3 variable allows precise frequency tuning.
• Typical application range is 1 MHz to 200 MHz. Used in VHF signal generators and frequency synthesizers.
• The BC547 or BFR91 transistor suits the Clapp for frequencies up to 100 MHz and 2 GHz respectively.
• Temperature coefficient of C3 determines long-term frequency drift. Using an NP0/C0G capacitor for C3 gives the best stability.

Quick Revision

• Clapp = Colpitts + C3 in series with L.
• Ceq = 1/(1/C1 + 1/C2 + 1/C3) ≈ C3 when C3 is smallest.
• f0 ≈ 1/(2π sqrt(LC3)). C3 controls frequency, C1 and C2 control feedback.
• C1 and C2 are large (1 nF range) to isolate the tank from transistor junction capacitances.
• Better frequency stability than Colpitts. Junction capacitance variation has minimal effect.
• Use NP0/C0G capacitor for C3 to minimize temperature drift.
• Feedback fraction β = C1/(C1+C2) (same formula as Colpitts).
• Exam trap: Students use Colpitts formula f0 = 1/(2π sqrt(L × C1C2/(C1+C2))) for Clapp. This is wrong. Clapp has three capacitors in the series arm: 1/Ceq = 1/C1+1/C2+1/C3.