Partially-premixed gas burner appliance, comprising: a combustion chamber, a fan being configured to provide an air flow to the combustion chamber, wherein the fan is assigned to an air inlet port of the combustion chamber or to an air duct being configured to provide the air to the air inlet port, an air flow restriction element being assigned to the air inlet port of the combustion chamber or to the air duct and being configured to provide a pressure drop so that the pressure downstream of the air flow restriction element is lower than the pressure upstream of the air flow restriction element, a gas modulator being configured to provide a gas flow to the combustion chamber, wherein a first portion of the air provided by the fan is premixed with the gas flow before the gas is combusted, wherein a second portion of the air provided by the fan is mixed with the gas while the gas is combusted, wherein the gas modulator is a pneumatic gas control valve configured to be used in a fully-premixed gas burner appliance, the pneumatic gas control valve having a main gas valve, a safety gas valve, a servo gas valve and gas outlet pressure regulator, wherein the gas outlet pressure regulator, namely a first chamber of the gas outlet pressure regulator in which a pressure is present that influences the nominal-value of the gas outlet pressure of the pneumatic gas control valve, is connected to the air inlet port or to the air duct upstream of the air flow restriction element such that the gas outlet pressure provided by the pneumatic gas control valve depends on the air pressure provided by the fan upstream of the air flow restriction element. a combustion chamber, a fan being configured to provide an air flow to the combustion chamber, wherein the fan is assigned to an air inlet port of the combustion chamber or to an air duct being configured to provide the air to the air inlet port, an air flow restriction element being assigned to the air inlet port of the combustion chamber or to the air duct and being configured to provide a pressure drop so that the pressure downstream of the air flow restriction element is lower than the pressure upstream of the air flow restriction element, a gas modulator being configured to provide a gas flow to the combustion chamber, wherein a first portion of the air provided by the fan is premixed with the gas flow before the gas is combusted, wherein a second portion of the air provided by the fan is mixed with the gas while the gas is combusted, wherein the gas modulator is a pneumatic gas control valve configured to be used in a fully-premixed gas burner appliance, the pneumatic gas control valve having a main gas valve, a safety gas valve, a servo gas valve and gas outlet pressure regulator, wherein the gas outlet pressure regulator, namely a first chamber of the gas outlet pressure regulator in which a pressure is present that influences the nominal-value of the gas outlet pressure of the pneumatic gas control valve, is connected to the air inlet port or to the air duct upstream of the air flow restriction element such that the gas outlet pressure provided by the pneumatic gas control valve depends on the air pressure provided by the fan upstream of the air flow restriction element. wherein a first portion of the air provided by the fan is premixed with the gas flow before the gas is combusted, wherein a second portion of the air provided by the fan is mixed with the gas while the gas is combusted, wherein the gas modulator is a pneumatic gas control valve configured to be used in a fully-premixed gas burner appliance, the pneumatic gas control valve having a main gas valve, a safety gas valve, a servo gas valve and gas outlet pressure regulator, wherein the gas outlet pressure regulator, namely a first chamber of the gas outlet pressure regulator in which a pressure is present that influences the nominal-value of the gas outlet pressure of the pneumatic gas control valve, is connected to the air inlet port or to the air duct upstream of the air flow restriction element such that the gas outlet pressure provided by the pneumatic gas control valve depends on the air pressure provided by the fan upstream of the air flow restriction element.