We report measurements of transfer functions and flux shifts of 20 on-chip high T$_C$ DC SQUIDs half of which were made purposely geometrically asymmetric. All of these SQUIDs were fabricated using standard high T$_C$ thin film technology and they were single layer ones, having 140 nm thickness of YBa$_2$Cu$_3$O$_{7-x}$ film deposited by laser ablation onto MgO bicrystal substrates with 24$^0$ misorientation angle. For every SQUID the parameters of its intrinsic asymmetry, i. e., the density of critical current and resistivity of every junction, were measured directly and independently. We showed that the main reason for the on-chip spreading of SQUIDs voltage-current and voltage-flux characteristics was the intrinsic asymmetry. We found that for SQUIDs with a relative large inductance ($L>120 $ pH) both the voltage modulation and the transfer function were not very sensitive to the junctions asymmetry, whereas SQUIDs with smaller inductance ($Lsimeq 65-75 $ pH) were more sensitive. The results obtained in the paper are important for the implementation in the sensitive instruments based on high T$_C$ SQUID arrays and gratings.
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