Nth-order arbitrary-phase-shift sinusoidal oscillator structure and analytical synthesis method of making the same

An oscillator, comprising:

• a first voltage node;
• a second voltage node;
• and
• two separated first, second and third grounded capacitors;
• and
• a first, a second and a third operational transconductance amplifiers (OTAs) connected in a serial sequence, wherein, each OTA has a particular transconductance value, and each OTA has a negative input, a positive input, at least two negative outputs, and at least two positive outputs, wherein
• one of the negative input and the positive input of each OTA is configured as a predetermined input, and the other of the negative input and the positive input of each OTA is configured as an alternate predetermined input, thus the predetermined input and the alternate predetermined input have opposite polarity signs;
• and
• the predetermined input and the alternate predetermined input of the first OTA are connected to first and fourth outputs, both of which have opposite polarity signs, respectively, of all OTAs, and are connected to the two separate first grounded capacitors, respectively, the two separate first grounded capacitors are connected to first and fourth outputs of the third OTA, respectively, the predetermined input and the alternate predetermined input of the second OTA are connected to second and third outputs, both of which have opposite polarity signs, respectively, of the first OTA, and connected to the two separate second grounded capacitors, and the predetermined input and the alternate predetermined input of the third OTA are connected to second and third outputs, both of which have opposite polarity signs, respectively, of the second OTA, and connected to the two separate third grounded capacitors.