It is well known that real op-amps do not share most of the desirable characteristics of an ideal one, particularly those of gain and output impedance. When presented with a capacitive load, such as a MOSFET or ADC, feedback in an op-amp circuit can quickly become unstable. This thesis studies and characterizes an op-amp’s output impedance and how its interaction with this type of load creates a parasitic pole which leads to instability. Applying ideas from feedback control theory, a model for studying the problem is developed from which a generalized method for compensating the undesirable circumstance is formulated.
Even in a zero-input state, many real op-amps driving capacitive loads can experience unforced oscillations. A case study is performed with three commonly used devices. First, the output impedance is determined by its dependence on the unity-gain bandwidth, load capacitance, and oscillation frequency. It is fitted into a second-order feedback control model that allows for an analytical study of the problem. It is then shown that a carefully designed passive network can be introduced between the load and op-amp to obtain a properly damped system free of oscillation and well-behaved.
Using a shunt resistor is a known and commonly used method for lowering an op-amp’s output impedance to gain stability. This work considers the converse addition of a series capacitor to instead lower the load capacitance seen by the op-amp, a seemingly complementary method that achieves the same goal. A generalized, composite compensation method is developed that uses both the shunt resistor and series capacitor– a strategy not yet found in literature. Relevant formulas for damping ratio and natural frequency are derived that allow the design of a passive compensation network. Furthermore, tradeoffs between compensation, voltage swing, current consumption, and power usage are considered.
An emphasis is placed on comparing simulated versus real circuits to highlight the fact that any problem is much worse in real-life than in a simulation. SPICE models and programs aim to de-idealize certain device characteristics, but often cannot account for environmental conditions and manufacturing variance. Thus, an importance is placed on experimental verification guided by simulations.
","abstract_html":"<p>It is well known that real op-amps do not share most of the desirable characteristics of an ideal one, particularly those of gain and output impedance. When presented with a capacitive load, such as a MOSFET or ADC, feedback in an op-amp circuit can quickly become unstable. This thesis studies and characterizes an op-amp’s output impedance and how its interaction with this type of load creates a parasitic pole which leads to instability. Applying ideas from feedback control theory, a model for studying the problem is developed from which a generalized method for compensating the undesirable circumstance is formulated.</p> <p>Even in a zero-input state, many real op-amps driving capacitive loads can experience unforced oscillations. A case study is performed with three commonly used devices. First, the output impedance is determined by its dependence on the unity-gain bandwidth, load capacitance, and oscillation frequency. It is fitted into a second-order feedback control model that allows for an analytical study of the problem. It is then shown that a carefully designed passive network can be introduced between the load and op-amp to obtain a properly damped system free of oscillation and well-behaved.</p> <p>Using a shunt resistor is a known and commonly used method for lowering an op-amp’s output impedance to gain stability. This work considers the converse addition of a series capacitor to instead lower the load capacitance seen by the op-amp, a seemingly complementary method that achieves the same goal. A generalized, composite compensation method is developed that uses both the shunt resistor and series capacitor– a strategy not yet found in literature. Relevant formulas for damping ratio and natural frequency are derived that allow the design of a passive compensation network. Furthermore, tradeoffs between compensation, voltage swing, current consumption, and power usage are considered.</p> <p>An emphasis is placed on comparing simulated versus real circuits to highlight the fact that any problem is much worse in real-life than in a simulation. SPICE models and programs aim to de-idealize certain device characteristics, but often cannot account for environmental conditions and manufacturing variance. Thus, an importance is placed on experimental verification guided by simulations.</p>","abstract_has_math":false,"creators":["Gandhi, Shubham"],"institution":null,"degree_name":"MS in Electrical Engineering","degree_level":null,"degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Vladimir Prodanov"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-03-01T08:00:00Z","date_published":"2016-03-01T08:00:00Z","updated_at":"2026-07-24T01:31:35Z","subjects":["op-amp","capacitive load","output impedance","stability","feedback","compensation","passive network","Controls and Control Theory","Electrical and Electronics","Electronic Devices and Semiconductor Manufacturing"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2016.13"],"render_values":[{"text":"10.15368/theses.2016.13","href":"https://doi.org/10.15368/theses.2016.13","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/1543","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Vladimir Prodanov"]},{"key":"dc:creator","label":"Author","values":["Gandhi, Shubham"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2017-03-09T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Electrical Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["op-amp","capacitive load","output impedance","stability","feedback","compensation","passive network","Controls and Control Theory","Electrical and Electronics","Electronic Devices and Semiconductor Manufacturing"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/1543","10.15368/theses.2016.13"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["It is well known that real op-amps do not share most of the desirable characteristics of an ideal one, particularly those of gain and output impedance. When presented with a capacitive load, such as a MOSFET or ADC, feedback in an op-amp circuit can quickly become unstable. This thesis studies and characterizes an op-amp’s output impedance and how its interaction with this type of load creates a parasitic pole which leads to instability. Applying ideas from feedback control theory, a model for studying the problem is developed from which a generalized method for compensating the undesirable circumstance is formulated.
Even in a zero-input state, many real op-amps driving capacitive loads can experience unforced oscillations. A case study is performed with three commonly used devices. First, the output impedance is determined by its dependence on the unity-gain bandwidth, load capacitance, and oscillation frequency. It is fitted into a second-order feedback control model that allows for an analytical study of the problem. It is then shown that a carefully designed passive network can be introduced between the load and op-amp to obtain a properly damped system free of oscillation and well-behaved.
Using a shunt resistor is a known and commonly used method for lowering an op-amp’s output impedance to gain stability. This work considers the converse addition of a series capacitor to instead lower the load capacitance seen by the op-amp, a seemingly complementary method that achieves the same goal. A generalized, composite compensation method is developed that uses both the shunt resistor and series capacitor– a strategy not yet found in literature. Relevant formulas for damping ratio and natural frequency are derived that allow the design of a passive compensation network. Furthermore, tradeoffs between compensation, voltage swing, current consumption, and power usage are considered.
An emphasis is placed on comparing simulated versus real circuits to highlight the fact that any problem is much worse in real-life than in a simulation. SPICE models and programs aim to de-idealize certain device characteristics, but often cannot account for environmental conditions and manufacturing variance. Thus, an importance is placed on experimental verification guided by simulations.
"]},{"key":"dc:title","label":"Title","values":["Out-of-Loop Compensation Method for Op-Amps Driving Heavy Capacitive Loads"]}]}],"canonical_facts":{"dc:contributor":["Vladimir Prodanov"],"dc:creator":["Gandhi, Shubham"],"dc:date.available":["2017-03-09T08:00:00Z"],"dc:description.abstract":["It is well known that real op-amps do not share most of the desirable characteristics of an ideal one, particularly those of gain and output impedance. When presented with a capacitive load, such as a MOSFET or ADC, feedback in an op-amp circuit can quickly become unstable. This thesis studies and characterizes an op-amp’s output impedance and how its interaction with this type of load creates a parasitic pole which leads to instability. Applying ideas from feedback control theory, a model for studying the problem is developed from which a generalized method for compensating the undesirable circumstance is formulated.
Even in a zero-input state, many real op-amps driving capacitive loads can experience unforced oscillations. A case study is performed with three commonly used devices. First, the output impedance is determined by its dependence on the unity-gain bandwidth, load capacitance, and oscillation frequency. It is fitted into a second-order feedback control model that allows for an analytical study of the problem. It is then shown that a carefully designed passive network can be introduced between the load and op-amp to obtain a properly damped system free of oscillation and well-behaved.
Using a shunt resistor is a known and commonly used method for lowering an op-amp’s output impedance to gain stability. This work considers the converse addition of a series capacitor to instead lower the load capacitance seen by the op-amp, a seemingly complementary method that achieves the same goal. A generalized, composite compensation method is developed that uses both the shunt resistor and series capacitor– a strategy not yet found in literature. Relevant formulas for damping ratio and natural frequency are derived that allow the design of a passive compensation network. Furthermore, tradeoffs between compensation, voltage swing, current consumption, and power usage are considered.
An emphasis is placed on comparing simulated versus real circuits to highlight the fact that any problem is much worse in real-life than in a simulation. SPICE models and programs aim to de-idealize certain device characteristics, but often cannot account for environmental conditions and manufacturing variance. Thus, an importance is placed on experimental verification guided by simulations.
"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/1543","10.15368/theses.2016.13"],"dc:subject":["op-amp","capacitive load","output impedance","stability","feedback","compensation","passive network","Controls and Control Theory","Electrical and Electronics","Electronic Devices and Semiconductor Manufacturing"],"dc:title":["Out-of-Loop Compensation Method for Op-Amps Driving Heavy Capacitive Loads"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_name":["MS in Electrical Engineering"]},"updated_at":"2026-07-24T01:31:35Z"}