Methods and apparatus to terminate transmission lines in voltage-controlled oscillators

An apparatus comprising:

• a supply terminal;
• bias network circuitry having a first terminal, a second terminal, and a third terminal, the first terminal of the bias network circuitry coupled to the supply terminal;
• a first transmission line having a first terminal and a second terminal;
• a second transmission line having a first terminal and a second terminal;
• a capacitor having a first terminal and a second terminal, the first terminal of the capacitor coupled to the second terminal of the bias network circuitry and the first terminal of the first transmission line, the second terminal of the capacitor is coupled to the third terminal of the bias network circuitry and the first terminal of the second transmission line;
• a first transistor having a first terminal and a control terminal;
• and
• a second transistor having a first terminal and a control terminal, the first terminal of the second transistor coupled to the second terminal of the second transmission line and the control terminal of the first transistor, the control terminal of the second transistor coupled to the second terminal of the first transmission line and the first terminal of the first transistor,
• wherein the bias network circuitry includes:
• a first inductor having a first terminal and a second terminal;
• a second inductor having a first terminal and a second terminal, the first terminal of the second inductor is coupled to the supply terminal and the first terminal of the first inductor;
• a first resistor having a first terminal and a second terminal, the first terminal of the first resistor is coupled to the second terminal of the first inductor, the second terminal of the first resistor is coupled to the first terminal of the first transmission line and the first terminal of the capacitor;
• and
• a second resistor having a first terminal and a second terminal, the first terminal of the second resistor is coupled to the second terminal of the second inductor, the second terminal of the second resistor is coupled to the first terminal of the second transmission line and the second terminal of the capacitor.

An apparatus comprising:

• a supply terminal;
• a first inductor coupled to the supply terminal;
• a second inductor coupled to the supply terminal;
• a first transmission line coupled to the first inductor, the first transmission line having a first resonant frequency, the first transmission line is configured to generate an output signal having a frequency based on the first resonant frequency;
• a second transmission line coupled to the second inductor, the second transmission line having a second resonant frequency;
• a first transistor coupled to the first transmission line and the second transmission line;
• a second transistor coupled to the first transmission line and the second transmission line, the second transistor is configured to control the first transistor based on the second resonant frequency of the second transmission line;
• and
• a first resistor coupled to the first inductor and the first transmission line, wherein the resistor is configured to reduce an amplitude of the first resonant frequency of the first transmission line,
• wherein the first transistor is configured to control the second transistor based on the first resonant frequency of the first transmission line.