As triangular voltage increases the voltage v₁ also increases. At t = T₁, when the voltage v_out becomes V_max, the voltage v₁ becomes equal to V_R and switching takes place. Therefore,


Similarly, when output voltage is +V_sat, the voltage v₁ is given by

As triangular voltage decreases the voltage v₁ also decreases. At t = T₂, when the voltage v_out becomes V_min, the voltage v₁ becomes equal to V_R and switching takes place. Therefore,


Therefore,

Solving the above equations, we get

The frequency f is independent of V_O, maximum frequency is limited either by slew rate or its maximum output current which determines the charging rate of C. Slowest speed is limited by the bias current of OPAMP.

If unequal sweep intervals T₁≠ T₂ are desired, then V_S can be changed. The positive sweep speed is given by (V_sat + V_S) / RC and the negative sweep speed is given by (V_sat -V_S)/ RC. The peak-to-peak triangular amplitude is unaffected by the voltage V_S.

Therefore,

Similarly, when the output voltage of first OPAMP is –V_sat, then

Therfore,

Therefore,

The oscillation frequency is given by

and the duty cycle is given by

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